So following Whitehead, it's appropriate to think of Plato as a philosopher of Organism.
Specifically, Plato wants explanations to have recourse to actual things that have a self-contained, internally harmonious composition. This is distinctive in comparison to presocratics who accepted explanations with recourse to the tropes or myths of popular speech (neither actual nor self-contained), or to elemental ontologies (these are explanations about emergent character, & so aren't self-contained).
(Note: In this reading, I'm going to ascribe to Plato an understanding of psyche that I've rolled together from my reading of Aristotle's De Anima, but I also think you can eschew this if you don't like it. My reading from Aristotle is of the psyche as the sphere of ultimate recourse of potential, and potential-of-potential, and so on in infinitum.)
SO Plato wants to say that among the presocratics, the Sophists are especially reprehensible, because they view the human psyche as this public thing that can be trans/formed by dialectic. And the problem for Plato is that this is very visibly demonstrated every day in the Assembly and courts of Athens. So Plato needs to respond to this with an account that covers a few bases:
* the role of rhetoric/language as something that shapes the individual and public
* a republic's nested sovereingty
(cont.) ... as the republic is a kind of sovereign that is comprised of human intellects, which are also sovereigns
So I think that the central conceit of The Republic, the holarchic
<https://en.wiktionary.org/wiki/holarchy> comparison between the human psyche and the polis, is in some way a response to the way that the presocratic sophists' rhetoric was effective at both the private and public levels. And by providing this holarchy, Plato is also able to demonstrate an interesting case of nested organisms.
In The Republic, Plato is famously willing to rewrite the eikon mythos so that the status-seeking (thymotic) part of humanity will be in an organic, supportive relationship with the rational part of the sovereign (whether psyche or polis).
Later on, in the thrall of the Pythagoreans, Plato was also willing to dispense with ordinary language in favor of abstract number as a purer handmaiden to the eikon logos. As he wrote, "He who is without mathematics shall not enter."
But I think that Plato was interested in demonstrating the process of pulling out special knowledge by pure inference from a single intellect. Socrates' real magic is in working out a proof with any willing audience. Socrates isn't pulling the answers from the common nomoi, as the rhetors were, but rather Socrates works from the self-contained answers of the individual.
This self-sufficiency is the true subject of Meno. This is also parallel with Charminides. And Socrates' failure in both cases demonstrates his explicit goals is actually a deeper refutation of the sophists' interest in gaining some kind of reductive nominal explanation of a humane topic of interest like arete (a sense of total excellence exclusively evident in a thriving example). Virtue is a virtue of organisms, not words. Dialogue can circle what is unspeakable but it cannot say it.
I am not a person who believes that Plato's point is a kind of infinite play of ironies. I think Plato had a specific ground for the ironic aporia of his dialogues. I think he was demonstrating that dialectic, if it's going to be a form of rhetoric, simply cannot produce virtue in an individual.
For Plato, rhetoric operates by drawing people along into illusions and word-games based on the non-harmonious operations of their internal faculties.
But a virtuous person has no such disharmony.
If I haven't made it plain already: this is the harmonious, organic composition of the Platonic psyche, according to the Republic.
The appetites (epithumia) sustain the animal body and so experiences appetites.
The esteem (thymos) sustains the social self and so experiences shame and glory.
The logos is that which is capable of abstracting from both the evaluation of appetite and glory. For this reason of trans-valuation, Socrates says that the logos must be in charge.
I think that there's a smug sense in which this gets misunderstood. Yeah, of course Plato is appealing to a special status for the philosopher. But he's actually saying that the reflective life has the capacity, the bandwidth for trans-valuation. There's' something so much more narrow about appetite and esteem: they're not really fit for trans-valuing values.
Towards the end of his career, Plato realizes that the same criteria of Organism that he sought in the polis and in the psyche are best ascribed to The World.
The World is the final ground of explanation, it is the final actual thing, it is the final self-contained thing, and it has the final internally harmonious composition. It is on the basis of the infinite, mutable changes of The World that the The World can be said to have a psyche -- which, recall, I'm defining as potential-of-potential
But furthermore, because The World has this potential-of-potential that is continually developed into Actuality along the lines of its internally harmonious composition, Plato attributes all these properties of The World to the transcendent act of patterning itself, the pattern of patterns, the form of forms. This is what the Timaeus is about.
So to be perfectly plain about it, Peirce doesn't think that there's much access to experience outside of the processing of these 3 aspects of significance: the fundamental character or quality of something; its clash with the character of something else; and whatever upshot emerges from the mediation of these two. The last item can then become the fundamental character of something else, and you can construct very complex structures of experience by chaining quiddities together like this.
But the stuff that Plato is interested in (laws from the inner necessity of an organism) can't be derived independent of a cosmos of character and relation. By attempting to think of all of the Just City, or of the mind, independent of its formation or context, is simply impossible.
That's why I think the "noble lie" at the heart of the Platonic pedagogy (for guardians) is seriously flawed. Plato is covering his tracks because none of this philosophy of organism actually can deal with generation
Plato's willing to rewrite ordinary language in this way because ordinary Greek is the source of so much sophistry in his eyes that even a "noble lie" is preferable to what is possible with intrinsic (entechnoi) rhetorical proof.
So what is to be made of the fact that Plato wrote in dialogues? That seems very sophist-ish. Rhetorical argument and such. There's a bunch of potential extraneous explanations, such as that it was simply the only form he knew, and so on.