In the Republic, where Plato develops his soul - city analogy, Plato never mentions that the three parts of the soul correspond to the three main goddesses that Homer talks about. They have the same roots, though. Gods and Goddesses can not only convince individuals to obey them, groups and whole communities can be under their influence. See here. In the Laws he goes a bit deeper into the theory of how he sees the gods. He calls it (or them) soul (Psychē) but we can be sure he means the same thing.
This is of course some distance away from Homer's gods. But the main feature, their moving us, is unchanged. Thus, they are forces. In the previous page we saw the domains of these forces. Homer makes it clear that they can act on both individuals and groups such as communities or armies. Plato develops this into his theories of the three parts of the human soul, and the three classes of people: the desiring class, i.e. the common people or 'money-earners', the aristocracy or guardians and the reasonable part, the ruler(s) or philosopher-kings.
Below is a visualization of the theory. It is somewhat simplified compared to the examples in Plato's writings but I believe this is his starting point. See e.g. Rep. 433B and the Philebus dialogue. Here he says that if we have found our "σωφροσύνης καὶ ἀνδρείας καὶ φρονήσεως", i.e. moderation, courage and prudence (the tamed versions of B, G and T) then what we have left is Justice. In other words: if an act is all three of these, then it must also be just.
Zeus is supposed to be in charge. He boasts of being stronger than all the other gods together but appears to avoid putting it to the test. See 'the golden rope', Il. 8.19. Hera is number two though she wants more, Athena is Tritogeneia, third-born (just as Zeus became first-born) and Aphrodite is fourth, though sometimes stronger than Zeus himself.
The solid red part is our Nomos, its border is Sophrosyne (moderation)
Note that there is some level-confusion about Sophrosyne (moderation)(1). In the text of Rep. 433B he uses the word as a limit only of the sensual desires, Aphrodite or the desiring part of the city. In other places (e.g. Charm 161B) he defines it the way Justice is defined here: doing one's own thing. In the picture above, moderation is the limit of the intersection of the three domains. This means, in Plato's view: Moderation is Justice. So what we have here is a bound Kronos: all gods in one but bound by moderation. Zeus has disappeared.