In the Republic, Plato lays out a psychological theory that includes a typology of polities and their corresponding citizens, which descend in order from Good to bad: Aristocracy, Timocracy, Oligarchy, Democracy, Tyranny. This has naturally been subject to all kinds of interpretation. Just sticking to the bare basics, it is common to read the characters in the Republic as representing these types or perhaps liminal states between them, and as moving up the typological scale as the dialogue progresses.
The Symposium has close ties to the Republic. Both are counted among the middle dialogues, there are clear similarities of imagery and doctrine, a unifying theme of ascent and descent, and moments hard not to read as direct interreference between them. It's also rich in characterization, with seven speakers giving monologues.
Now, seven does not equal five, but it still seems obvious to ask whether the typological psychology from the Republic can be applied to the speakers of the Symposium. I've tried several schemes myself, but the closest I've gotten is a "hm, well maybe..." Nothing very satisfying.
TL;DR: Have any interpreters of Plato tried to apply the typological psychology of the Republic to the characters in the Symposium? If so, how'd it go, and where can I find their work? Anyone who wants to take a crack at it here is also welcome.