Nagy and Collins are right to associate ὑπολαμβάνω as a verb of speaking with contexts of competitive verbal exchange. For, as we shall see, ὑπολαβὼν ἔφη most commonly signifies the final trumping or capping response of one speaker to another in the context of the aggressive verbal dueling of two partners in dialogue.  But I would part company with Collins in his restriction of this formula to the context of rhapsodic performance and competition at festivals. Instead, I shall argue, ὑπολαβὼν ἔφη seems to be in origin a lively, colloquial, and perhaps subliterary expression linked to low or popular prose storytelling. For, strikingly, this quotative formula occurs over thirty times in just this meaning in the late collections of Aesop’s fables, so that one fable scholar has even identified ὑπολαβὼν ἔφη and its later lexical replacement ὑποτυχὼν ἔφη as “fable formulae.” 
I. Fifth-Century Occurrences and Fable Usage
With this, their direct speech ends and we return to the main narrative—the enactment of the queen’s plot.
At the time, the Lemnians’ posed adunaton ends negotiation. But many years later, Herodotus informs us, when Miltiades son of Cimon gets possession of the Thracian Chersonese for Athens, he is able to fulfill the paradoxical terms of the Lemnian response by sailing from there, and so takes over the island.
And with Xerxes’ sage words, the entire episode ends.
Here, the moment at which the fable shifts to direct discourse for the trumping response of the birds is marked by the speech formula αἱ δὲ ὑποτυχοῦσαι … ἔφασαν.  The verb ὑποτυγχάνω is entirely post-classical in preserved Greek texts, and, even in later periods, rare in literary prose.  It occurs, however, nearly forty times in fables in the late fable collections, always in the fixed form aorist participle plus verb of speaking, and always in exactly this context of a witty, trumping riposte to an interlocutor that ends discussion. 
The text here follows Perry’s edition; but note that in all three different versions Chambry prints, the fox’s punchline is slightly different. According to the apparatus criticus of Chambry 1925–26, several mss of his tradition I (Pg, Mb, Me, Mf), as well as all the mss of his traditions II and III read ὑπολαβοῦσα ἔφη or simply ὑπολαβοῦσα instead of ὑποτυχοῦσα ἔφη or just ἔφη. As in all but two of the fables that use this formula, the fox’s ὑποτυχοῦσα ἔφη here marks the moment of shift from indirect to direct speech, while in all the fables in which it occurs, the formula marks the fable’s “punchline” or last word.  And here, in contrast to the simpler version of “The Cat and the Birds,” we find another feature very characteristic of the fable uses: the fox’s retort to the crocodile wittily turns the latter’s own words against him, transforming the boastful reptile’s γεγυμνασιαρχηκότων (ancestors who were gymnasiarchs) into the insulting γυμνασμάτων (his tough, unsightly hide revealing the many “work-outs” [i.e. beatings] he’s received; or perhaps the crocodile’s leathery skin suggests sun damage?).
Here too, one of the several manuscripts that preserve this fable (Mb), reads ὑπολαβοῦσα ἔφη in place of ὑποτυχοῦσα ἔφη, while another manuscript (Pc) omits ὑποτυχοῦσα entirely, reading simply καὶ ἡ ὗς ἔφη. And here again, with a shift from indirect to direct speech, ὑποτυχοῦσα ἔφη introduces the fable’s internal “punchline,” in which the sow cleverly transforms the bitch’s abuse into its opposite, claiming the special favor of Aphrodite and thereby winning the argument and shutting down any further discussion. I offer this particular example because here the epimythion or moral external to the fable furnishes a veritable gloss on the function of the speech formula ὑποτυχοῦσα/ὑπολαβοῦσα ἔφη: οὕτως οἱ φρόνιμοι τῶν ῥητόρων πολλάκις καὶ τὰ ὑπὸ τῶν ἐχθρῶν φερόμενα ὀνείδη εἰς ἐπαίνους μετασχηματίζουσι. (“So it is that clever public speakers often transform even the abuses hurled at them by enemies into praise.”)
In this allegorical fable—Horkos punishing the wicked in his own time—we find the same alternation between ὑποτυχών and ὑπολαβών marking Oath’s climactic response among the manuscripts. Thus, of the five manuscripts that preserve this fable, four (Pf, Me, Mf, Ma) read ὑποτυχών alone or ὑποτυχὼν ἔφη, while one manuscript (Mb) instead reads ὑπολαβὼν ἔφη.
This is a rare and remarkable sequence in Thucydidean narrative. Rather than set speeches by kings or generals addressing their troops, foreign ambassadors, or civic assemblies, here two Everymen, anonymous combatants, engage in a brief rapid-fire dialogue. In this context, ὑπολαβών…εἶπεν marks what the questioner himself regards as a decisive retort to the befuddled herald, its colloquial vigor reinforced by the sharp, slangy deictic ταυτί.  In the event, this retort does not end discussion because of the complementary misprision of the two speakers—the poor herald assuming there was only one battle; the anonymous interlocutor assuming that the herald represents the group defeated in the second battle. But as the rapid-fire back-and-forth continues, we get another striking colloquial feature: for the last two exchanges, verbs of speaking entirely disappear and we are given simply quoted dialogue, evoking lively oral narrative or performance.  Finally, the narrator’s brief editorial comment at the end of the episode explains and motivates this highly unusual instance of Thucydidean enargeia: unable plausibly to convey the “suffering” (πάθος) of the Ambraciots through a coolly objective numerical reckoning of the dead, the narrator instead gives vividness and heft to their misfortune through the lively, colloquial exchange of ordinary citizens. 
Here again, the Lacedemonians offer what they consider a decisive retort to the Eleans within a barbed and testy exchange (introduced by ὑπελάμβανον), but the Eleans reject this bit of Spartan logic-splicing and stick to their position.  In this context, we should perhaps understand the anomalous imperfect tense of ὑπελάμβανον as conative: the Lacedemonians “were trying to trump [the Eleans] in argument,” but (Thucydides implies by the use of the imperfect), they failed. 
Translators of Thucydides regularly construe ὑπολαβών εἶπεν here to mean that Archidamus “interrupted” the Plataeans in the midst of their appeal, but there is no justification for this interpretation.  The Plataeans’ appeal is in fact complete in one short paragraph, beginning and ending with mention of the Spartan king Pausanias and his promise “to let them live autonomously.” Furthermore, the aorist participle εἰπόντων signifies that they are done speaking.  Instead, ὑπολαβὼν εἶπεν signifies Archidamus’ aggressive, trumping response, which carefully picks up all the terms and ideas of the Plataeans and turns them against the hapless ambassadors. And, characteristically, Archidamus’ sharp, decisive response shuts down the discussion—without a word, the ambassadors go back to their city to communicate his message to the populace and get further instructions (Thucydides 2.72.2).
Commentators have noted how carefully and self-consciously Thucydides has his anonymous representative figures here lay out the form and parameters of the speaking situation; as Simon Hornblower notes, “The invitation, in this para. to a dispute in dialogue form is expressed in a remarkably self-conscious manner, using what may have been the technical language of rhetoric; ῥῆσις is used only here in Th. It is almost as if Th. has self-referentially stepped outside the constraints of his ‘genre’ to explain what he is doing.”  H. Ll. Hudson Williams in 1950 had already pointed out that the alternatives the Athenians pose of long, uninterrupted speeches or rapid-fire dialogue precisely correspond to (and presumably derive from) the Sophistic system of epideictic makrologia vs. dialectic question and answer (as we see it represented also in several Platonic dialogues).  And indeed, this is precisely what is expressed in the Athenians’ proposal by the participle ὑπολαμβάνοντες, which here by itself seems to mean “in dialogue” or “in response.”  Given the context, it is tempting to suggest that the use of ὑπολαμβάνω in this sense may itself have developed in Sophistic circles, picked up from colloquial or popular narrative contexts and made into a technical term for rapid-fire dialogue and debate (in this sense, perhaps a term of art, like ῥῆσις?) Indeed, it is remarkable that, after a single verb of answering at 5.86 (οἱ δὲ Μηλίων ξύνεδροι ἀπεκρίναντο), Thucydides abandons the narrative frame altogether, offering simply the direct speeches of the two participants, in a form that mimes high drama or the lowest forms of colloquial narrative.  At the same time, it would be a mistake to imagine that in such a semantic development, ὑπολαμβάνω has lost its competitive, aggressive edge. For the Melian Dialogue—like all Sophistic debates—is a competition in which each participant in the exchange is fighting desperately to win. As Colin Macleod puts it, “It is a battle, as their choice of vocabulary implies …”  In light of the parallels, the present tense of the participle is unusual here; we almost always find the aorist ὑπολαβών or ὑπολαβόντες. Perhaps in this instance, the present participle signifies repeated responses in dialogue (just as καθ᾿ ἕκαστον does)?
II. Fourth-Century Occurrences
It is easy to see how the use of ὑπολαμβάνω for such a hypothetical, anonymous heckling question continues the usages we have already considered, for here, rather than offering a decisive response that shuts down further discussion, the imaginary heckler raises a question meant to stop the interlocutor in his tracks.  In this context in the Hellenica, the imaginary question briefly but effectively transforms monologue into rapid-fire verbal dueling between two, in which the imaginary speaker thinks to triumph with a decisive question or objection. And it is surely no accident that Xenophon represents this challenge as doubly embedded in direct speech, for it points to the colloquial origins for this kind of aggressive verbal sniping, here artfully included for maximal mimetic vigor and rhetorical punch. 
Xenophon goes on to remind him in sharp terms of the king’s initial demand that they lay down their arms; his willingness to make a truce and provide them with necessary supplies when they refused to do so; his treacherous capture of their commanders come to parley with him under truce; and the commanders’ subsequent torture and death. Xenophon ends this speech by turning to address the other troop commanders, urging them to strip Apollonides of his command and demote him to a baggage-carrier:
Here again, in a complex speech situation with multiple potential speakers, ὑπολαβὼν ἔλεξεν/ εἶπεν twice marks the moment at which one individual out of many assertively claims the discursive floor—used first for Xenophon’s impatient interruption (which is explicitly flagged as such), and then again for Hagesias’ attack based on Apollonides’ shockingly ungreek practice of wearing earrings. Still, even if this represents a new use or extension of usage, we might note that, in common with many other uses of ὑπολαβών as a verb of speaking, the exchange here is a barbed and hostile one and that both Xenophon and Hagesias in different ways trump Apollonides’ utterance and shut down all further discussion.  Thus for Xenophon, this use of ὑπολαβών serves his narrative and mimetic purposes, allowing him to capture complex, unpredictable, and dynamic speech situations in lucid prose.
And Socrates proceeds to explain to Protagoras that he wants a more substantive answer, on the model of, “From Zeuxippus, one would learn painting” (Protagoras 318b4–d4).
And so, more or less against Protagoras’ initial intent and expectation, the dialogue as a whole unspools.
The verb ὑπολαμβάνω here marks the bluntly abusive and decisive answer that Socrates and Glaucon would together deliver to their hypothetical naïve interlocutor; thus note especially Socrates’ use of εὐήθης to characterize this interlocutor as a “simpleton.” At the same time, this passage provides a good example of one striking feature of ὑπολαμβάνω as a verb of speaking in Plato: this verb is never applied directly to Socrates in his own person in real dialogue. Presumably, it is simply too snarky, aggressive, or competitive to characterize the speech of Socrates as the ideal conversationalist. Instead, Socrates uses it (as here) only in hypothetical contexts and imagined exchanges.
This imagined exchange then leads directly to the heart of Socrates’ defense—that he possesses “human wisdom” precisely to the extent of knowing that he knows nothing, and that he will support this claim with the Delphic god himself as witness (Apology 20d4–21a). 
Here, Socrates sets himself up as Gorgias’ argumentative ally, assisting him against the snide and forceful attack of an anonymous questioner. And that this is an aggressive, heckling question, Socrates makes perfectly clear by his parenthetic addition, “if he wished to give you a hard time/be annoying in argument” (εἰ βούλοιτο δυσχεραίνειν ἐν τοῖς λόγοις). Here Plato offers a metadiscursive gloss or commentary that is apt for all the occurrences of ὑπολαμβάνω in this meaning. 
Polemarchus leaps in, replacing his father with a heated counterattack on Socrates’ position.  Indeed, I would venture to suggest that the use of ἔφη…ὑπολαβών as an introductory formula here signifies that Polemarchus himself imagines that he is offering a decisive, trumping response, invoking the authority of Simonides just as his father had earlier quoted Pindar (Republic 331a2–10). But Polemarchus with his old-fashioned style of quoting traditional authorities is no match for newfangled Socratic dialectic, and he is soon caught in his turn in the coils of yet another refutation.
The lack of “sauce” or “meat” (ὄψον) may seem a minor issue, but in fact it leads directly into Glaucon’s complaint that Socrates imagines “a city of pigs” (Republic 372d4), which in turn precipitates a fullscale revision of the imagined city on Socrates’ part. In just the same way at the beginning of Book 4, Adeimantus intervenes, when Socrates has just concluded a lengthy exchange with Glaucon about the education and proper lifestyle of the city’s guardians:
Adeimantus’ objection—or legal “accusation,” as he styles it—requires Socrates to engage in an extended dialectical consideration of the dangers presented by wealth and luxury to different contingents within the city and therefore to the city as a whole, before he can pronounce the “city in words” fully constructed at Republic 5.472d. ὑπολαμβάνω does this same kind of work at Republic 8.544b1 (its last occurrence in this meaning in the Republic). Here, ὑπέλαβε refers back to the complicated stage business at the beginning of Book 5 (449b–450a) by which Polemarchus and Adeimantus whisper together, object, and divert the course of discussion by demanding a full account of what Socrates means by his glancing reference to women and children being held in common.
III. Some Speculations on Etymology, or Dialogue as a Contact Sport
“οὕτως ἀγεννής,” φησί, “καὶ φόβου πλήρης
All of this suggests that the ancients perceived an overlap in semantic spheres of the two verbs, and already espoused different interpretations of the meaning of the Iliad passage. For some (like Babrius), ὑποβλήδην … φησι was understood to be a poetic or epic equivalent of ὑπολαβὼν ἔφη, signifying not interruption but a final aggressive, trumping response in dialogue between two. In just the same way, the use of ὑποβλήδην by Apollonius Rhodius and Quintus of Smyrna suggests that they understood ὑποβλήδην in Iliad 1 to mean simply “in response” (without interruption), or perhaps (as Gottfried Hermann argued in 1834) as “responding with admonition/advice.” I am therefore inclined to accept that the terms ὑποβλήδην/ὑποβάλλειν do mean “interrupt” in the Iliad, but also to acknowledge that the later meaning of ὑποβλήδην is uncertain.  Nonetheless, given various ancient authors’ perception of an overlap in semantic sphere of these two terms, any etymological account offered of the semantics of ὑπολαμβάνω/ὑποτυγχάνω should also apply to ὑποβλήδην/ὑποβάλλω.
|ὑπολαβὼν ἔφη/εἶπε||Herodotus, Thucydides, Xenophon, Plato, Demosthenes, Hyperides, Machon, Aesopic fable|
|ὑπαρπάσας … εἶπε||Herodotus|
|ὑφαρπάσας … ἔφη||Plato Euthydemus|
|ὑποθωπεύσας … λέγει||Herodotus [1.30.3]|
|λέγειν ὑπομαλακιζομένους||Xenophon [Anabasis 2.1.14]|
|ὑποτυχών … ἔφη/εἶπε||Josephus, Dionysius of Halicarnassus, Plutarch, the Suda, Aesopic fable|
|εἶπεν ὑπομειδιάσας||Aesopic fable (no. 284 Perry)|
The overwhelming number of these phrases occur in dialogue between two speakers or two constituencies, and with the sole exception of the phrase in Xenophon’s Anabasis, they combine a coincidental aorist participle with a main verb of speaking.  I would contend that in all these instances, the preverb ὑπο- signifies “in answer, in response” in dialogue, so that the participle and main verb must be taken as a single semantic unit, signifying “said in answer/responded x-ingly.” Thus for example, in the passage from Xenophon’s Anabasis quoted above, the hapax ὑπομαλακίζομαι can hardly mean “to grow cowardly by degrees,” as it is glossed in LSJ. (As in, “others [ἄλλους] became gradually cowardly as they were speaking”?!) Instead it means that, in contrast to the named speakers Cleanor, Proxenus, and Theopompus, who have just offered resistant and defiant answers to Phalinus, some unnamed others “spoke gently or conciliatingly in answer.”  In like manner, in the famous encounter of Solon and Croesus, at the moment Solon launches into his response to Croesus’ question, “Who of mortals have you seen who is the most blessed?,” Herodotus characterizes his style of answering thus: Σόλων δὲ οὐδὲν ὑποθωπεύσας, ἀλλὰ τῷ ἐόντι χρησάμενος λέγει· (Herodotus 1.30.3). ὑποθωπεύσας here does not mean “delicately flatter,” as Powell glosses it in his Lexicon to Herodotus, evidently trying to capture the nuance added to the verb by the preverb ὑπο- (since, after all, what Croesus wants is not “delicate flattery,” but blatant flattery).  Instead, Herodotus’ words mean “Solon, not flattering him at all in response, but using only the truth, says …”
IV. Euthydemus: How to Do (Mean) Things with Words
Collins is certainly right to emphasize the competitive quality of verbal exchanges in the Euthydemus, but I would contend that it is a mistake to limit Plato’s sources and influences to the performance of poetic genres. We must also reckon with low colloquial prose forms like fable and other popular oral narratives, and in the case of the formula ὑπολαβὼν ἔφη, these are much more likely to be Plato’s inspiration than the orderly rotation of rhapsodes performing at the Panathenaia. 
Here ὑπολαβών functions just as it does in Herodotus and in fable, to mark the final response of an interlocutor in a dialogue of two by which he trumps his opponent and shuts down discussion. In the same way, when Dionysodorus has been conducting an argument with Ctesippus to prove that because Ctesippus has a dog that has puppies and he has a father, the dog is his father and the puppies his brothers, Dionysodorus intervenes at the end of the sequence before Ctesippus has a chance to answer his last question, interposing a final devastating question:
Three more times, the phrase occurs with a change of speaker at the decisive, clinching moment of argument, as the two brothers Euthydemus and Dionysodorus work together as a kind of eristic tag-team.  A good example is 298b1, where Dionysodorus has been developing an argument with Socrates about fathers and brothers, demonstrating that there is a logical contradiction if Socrates’ brother Patrocles is also “other than his brother” (because not by the same father), or his father Sophroniscus is “other than a father” (because not the father of Patrocles, who is the son of Chaeredemus; Euthydemus 297e1–298a9). At this point, Euthydemus intervenes to deliver the argumentative coup de grâce:
This is a moment where the argument goes just as the brothers Dionysodorus and Euthydemus wish, but on a couple other occasions, they are outmaneuvered by Socrates’ dialectical skill. At these junctures, ὑπολαβών marks the trading off from one brother to another not to shut down an argument entirely, but to change the rules of engagement or shift the topic. Thus early on, Socrates lures both brothers into an argument, versions of which he says he has heard in the past from “those around Protagoras and others even older” (Euthydemus 286c2–3). Since Dionysodorus has claimed to Ctesippus that there is no such thing as refutation (ἀντιλέγειν), Socrates leads the brothers on to affirm that therefore there is no such thing as lying or false opinion or ignorance or doing wrong of any kind. At this point, Socrates is conducting the conversation with Euthydemus, and now he springs the trap:
Here Dionysodorus interposes, resorting to simple abuse to short-circuit this damning line of argument, and then insisting that the brothers should not be held accountable for things they had said earlier.  When this does not put Socrates off, Dionysodorus attempts to shift the ground of argument entirely by latching onto Socrates’ phrase “what else does this argument intend to say” (τί σοι ἄλλο νοεῖ τοῦτο τὸ ῥῆμα), also at this point changing the rules of engagement by insisting that Socrates answer a new question before he (Dionysodorus) has answered Socrates (Euthydemus 287b6–d6).
Here Euthydemus (the sharper brother  ) recognizes that Dionysodorus is headed for trouble and warns him. When Socrates tries to engage Euthydemus on the same argumentative trajectory, Dionysodorus again aggressively intervenes, trying to latch onto Socrates’ mention of “brother” to shift to an entirely new argument.
In fact, Dionysodorus has blundered again in the heat of argument and set the brothers up for refutation by contradiction, as Ctesippus immediately points out in his gloating address to Euthydemus. And as Socrates notes, Ctesippus has beaten the two brothers by turning against them their own techniques of argument. But what I want to call attention to in this passage is the use of the phrase ἔφη ὑφαρπάσας in exactly the same context and with the same semantics that we would expect from ἔφη ὑπολαβών—marking the moment a new speaker intervenes to claim the discursive floor and cap the argument. From this we may conclude two things: that ὑφαρπάσας signifies even more aggressive verbal sniping than ὑπολαβών  , while this substitution in turn strongly suggests that the semantics of the second elements of these verbal compounds were still palpable at the time Plato was writing.
Socrates then continues and elaborates the imagery of dance almost immediately as his narrative proceeds:
Here Euthydemus nimbly emerges as a virtuoso soloist from the choral throng of his admirers, giving the argument a double twist like some complex dance-step.  And very soon he is joined in the spotlight by his brother Dionysodorus:
A whole complex of terms here irresistibly evokes the virtuoso dance performance of the Phaeacians Halius and Laodamas in Odyssey 8 (an evocation that itself tends to confirm that all Socrates’ separate imagistic elements of dance and ballplaying are meant to be taken together).  We recall that in Odyssey 8, immediately after an elaborate choral dance, the two royal brothers Halius and Laodamas are bidden by their father Alcinous to perform alone, “since no one vied with them”:
πορφυρέην—τήν σφιν Πόλυβος ποίησε δαΐφρων—
τὴν ἕτερος ῥίπτασκε ποτὶ νέφεα σκιόεντα
ἰδνωθεὶς ὀπίσω· ὁ δ᾿ ἀπὸ χθονὸς ὑψόσ᾿ ἀερθεὶς
ῥηϊδίως μεθέλεσκε, πάρος ποσὶν οὖδας ἱκέσθαι.
αὐτὰρ ἐπεὶ δὴ σφαίρῃ ἀν᾿ ἰθὺν πειρήσαντο,
ὀρχείσθην δὴ ἔπειτα ποτὶ χθονὶ πουλυβοτείρῃ
ταρφέ᾿ ἀμειβομένω· κοῦροι δ᾿ ἐπελήκεον ἄλλοι
ἑσταότες κατ᾿ ἀγῶνα, πολὺς δ᾿ ὑπὸ κόμπος ὀρώρει.
Both the context and Plato’s explicit metadiscursive image ὥσπερ σφαῖραν ἐκδεξάμενος τὸν λόγον make absolutely clear the semantic or conceptual sphere from which the participle ἐκδεξάμενος is borrowed: as E. H. Gifford noted long ago, it is “a metaphor from catching a ball or anything passed from hand to hand.”  But Plato has also introduced one significant divergence from his Odyssean model that gives a sudden darker nuance to the image: rather than just artfully passing the ball back and forth while twisting, leaping, and dancing, the sophistic brothers make it into a weapon by aiming it at the hapless youth Clinias. 
Notice first that, already with the image of Corybants, there is a hint that the brothers’ verbal “dancing” has become wilder, less structured, and perhaps a bit dangerous.  But Socrates then goes further in the course of the same speech:
Here the “enthronement” (θρόνωσις) of the initiand unnervingly morphs into the “stool” (σκολύθρια) yanked out from under the unsuspecting butt of a practical joke, as dance and play (παιδιά, παίζοντε) turn into mean-spirited and potentially harmful “mockery” and “practical joking” (προσπαίζειν). 
Within this playful mythological imagery lurks the threat of bodily dissolution, as Dionysodorus and Euthydemus are imagined to chop their interlocutors in pieces and skin them alive. 
Socrates, after his consistent (if occasionally barbed) effusions about the wondrous wisdom of the sophistic brothers, is scathing on the subject of this smug logographer, in an effort to defend “the thing itself” (philosophy) against his scornful dismissal. Thus he characterizes the man as one of those
Socrates goes on to argue that such men are in fact inferior to both philosophers and statesmen and “while they are actually in third place, they seek to seem to be first” (306c5).