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The basic idea of polytheism can be summed up in a single word, very short and very common: "Who".
We use the term "who", or equivalent terms in many, many languages, to refer to unique individuals.
The fact that we, on a very fundamental level of language usage, recognize a distinction between "who" and "what" provides the metaphysical framework for unique individuals not determined by ontic coordinates.
Were they determined wholly by ontic coordinates, every who would, by virtue of that, be a "what", and would be designated not by a proper name, but by a common noun.
Even if every "who" we can think of is also in some respect--or in many respects--a "what", we can think a category of "who" unrestricted by whatness.
In the technical language of Platonism, a "who" unrestricted by whatness is a supra-essential unit (huperousios henas); and this is the definition of a God.
The number of such "whos", by definition, cannot be determined through essence or whatness; They can only give themselves in the pure positivity of appearance, theophany.
Mutatis mutandis, we can only actually know a mortal "who" by acquaintance; and many languages recognize this through distinguishing the knowledge of facts and essences ("whats") from the knowledge of "whos" (e.g. French savoir vs. connaitre).
One question people tend to have about this account is, why the Platonists didn't explain this stuff in terms of "who" and "what" instead of in terms of kinds of unit.
To some degree, of course, they did, if you can unpack their technical language a bit; e.g., their concept of "essence" has "whatness" embedded in it, and so if you start thinking about what is actually "supra-essential", you start to get to what is beyond "what".
But the main reason they didn't is because they weren't arguing *to* the Gods, but *from* Them, as a basis. Since it was pre-theoretically given in their culture that the Gods were *persons* not bound by space or time, they could *use* this preconception to argue to other points.
This is a point that Richard Bodéüs makes about Aristotle, by the way: that Aristotle uses mainstream, uncontroversial theses of Hellenic theology, what he calls "the theology of living immortals", to argue toward other, non-theological theses.
