Dueling Homer: Duals at Twenty Paces
It is probably a matter of taste—it is to my taste—to see part of the unity here as Dumezilian with Agamemnon/Odysseus being, first function, Diomedes/Ajax being second, both enclosing the third function Phoenix/Nestor. But Dumezilians might be unhappy with placing Nestor in the second function. And many others would wonder if this kind of analysis is necessary. Maybe not, but isn’t it neat? In any case, the text as it stands works, even with the duals, and were it not for the duals the structure of Iliad 9 would hardly be in question.
The Literary Coherence of the Ambassador Sequence
To put it in nar ratalogical terms, when the text of Iliad 9 presents a narrator introducing a reference to the “quarrel between Odysseus and Achilles,” most strikingly through the use of those duals, the narratee here is the audience of the Iliad but not as the receiver of the plot of the Iliad’s narrative; the relationship between narrator and addressee occurs in what I am now calling a kind of 4th person address: there is an implied traditional audience, one, that, by definition, always has the same tradition-horde as that of the implied traditional narrator. Thus, at moments like the use of the dual in Achilles’ address to the members of the embassy, the communication introduces into the plotted narrative a higher-order bit of narrative, from the tradition-hoard that competent singers and hearers have as part of their working knowledge. Compare this way of looking at the phenomenon from Best of the Achaeans (Chapter 3 §19 [emphasis mine]):
The Literary Use of Tradition’s Boor
ὡς δὴ τοῦδ’ ἕνεκά σφιν ἑκηβόλος ἄλγεα τεύχει,
οὕνεκ’ ἐγὼ κούρης Χρυσηίδος ἀγλά’ ἄποινα
οὐκ ἔθελον δέξασθαι, ἐπεί πολὺ βούλομαι αὐτὴν
οἴκοι ἔχειν. καὶ γάρ ῥα Κλυταιμνήστρης προβέβουλα
κουριδίης ἀλόχου, ἐπεὶ οὔ ἑθέν ἐστι χερείων,
οὐ δέμας οὐδὲ φυήν, οὔτ’ ἄρ φρένας οὔτε τι ἔργα.
In this passage, everyone notices Agamemnon’s gratuitous slap at his wife as he over-praises Chryseis. Α psychological reading is, of course, readily available, one that exploits Agamemnon’s boorishness towards Clytemnestra: Agamemnon seems to be acting true to form here. But while one can note psychological acuity of the narrative, I point in this context to the fact that the narrator has also introduced a major part of the tradition of the Trojan War, namely the traditionally deep problems with the House Atreus, usually abbreviated to the term “the curse of the house of Atreus.” The important point for my discussion is that Agamemnon’s slight points to the array of narratival material regarding the curse of the House of Atreus, which has nothing to do with the quarrel as it is developing between Achilles and Agamemnon in Book 1. Yet readers “feel” the slight as having an ironic tinge: I certainly wince when I think of Clytemestra “hearing” within the resonance of tradition this slight at a distance; certainly anyone familiar with the tradition in any sense of the term, “hears” the allusion. And I would believe it to be a very peculiar reader of Homer who can resist reading here the irony that awaits Agamemnon in his homecoming bath. I mean to say that though this allusion presents no “textual” problems (as does the use of the duals in Il. 9), the same theoretical problem exists, as existed for the duals in Iliad 9. To put the matter directly, I suggest that the passage in Iliad 1 where the narrator introduces the curse of the house of Atreus is strikingly similar to the way the narrator introduces the quarrel between Achilles and Odysseus in Iliad 9 because the immediate narrative is opened up for a reference to the tradition at large.
A Second Example
Χρυσόθεμισ καὶ Λαοδίκη καὶ Ἰφιάνασσα.
In this catalogue of daughters, the girl who receives the important attention is the last, Iphianassa. As noted above, commentators have in the past liked to declare this list of daughters as proof-positive that Homer “does not know” the story of Iphigeneia. That is to say, the difference in name is, with a scholarly commonsense gesture, equated with an absolute difference in character. It may be, however, that the poetics of Homeric naming is different than that for which such a calculus calls. For example, would one say that Homer didn’t know the story of Jocasta and Oedipus because in Od. xi, Oedipus’s wife is called Epikasta? Probably not—I hope.
There are other ways to set out the parallels, but this gives you the general idea. These stories are doublets of one another. There are, it seems to me, sufficient similarities between the stories to shift the burden of proof from readers like me who want to say that the offer is an allusion to the story of Iphigeneia to those who claim that Agamemnon’s ruse of a marriage between Achilles and a daughter of Agamemnon (named Iphi-anassa) is not related to the ruse of a marriage between Achilles and a daughter of Agamemnon (named Iphi-geneia), where both ruses are designed to move the Achaeans from a position of stasis incurred by Agamemnon’s slighting of an important figure (in the one case the gods (specifically, Artemis) and in the other case the son of a god (Achilles).
A Kind of Meaning
“Not even if his own mother died and his father.”
χαλκῷ δηιόῳεν, ὅ δ’ ὀφθαλμοῖσιν ὁρῷτο (Odyssey 4.225–226)
“Not if before his very eyes they cut down a brother or a beloved son.”
Thus one part of the Helen’s Cup passage refers to an Iliadic context, the other to an Odyssean context.
Individual Lines that Assert the Merisim, Iliad + Odyssey
Ιn each of the above examples, the highlighted part of the line refers to an Iliadic tradition and the other, printed in boldface, to an Odyssean tradition. There are other examples, but at this point it is time to ask: What we are to make of this? One way of looking at these examples is to say that the poem, without referring to performances, or texts, or any other kind of micro verbal artistry, is alluding to the very elements of the Homeric tradition that have survived to us as intact: namely, the Iliad and the Odyssey. 
|Il. 1. ff. Council of the Achaeans
|Od. 2.1 ff Council of the gods
|Il. 9.189 ff.—Achilles’ song
|Od. 9.1 ff.—Odysseus’s song
|Il. 10. Doloneia
|Od. 11. Nekuia
|Il. 19.397 ff. Achilles’ horses
|Od. 17.291 ff. Odysseus’s dog, Argos 
|Il. 24—Priams’s encounter with Achilles
|Od. 24—Laertes’ encounter with Odysseus
The ellipses points will be filled in after I make my main point, namely, that cooperation, collaboration, or some sense of a collective project is necessary to understand the aesthetic unity of the poems. Frame argues for a creation of the poems as we have them at The Festival of the Panionia, and I find the argument he makes compelling. Needless to say, I cannot do justice right now to the analysis he deploys to support his hypothesis; what I really need for my purposes is the notion that the poems are a unity (Frame 2009:560):