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.
This is of course some distance away from Homer's gods. But the main feature, their moving us,
is unchanged. The all-important difference is that Plato's god(s) must be absolutely good
and reasonable - the evil ones he does not talk about anymore. Homer's gods, except Zeus, are monofocal: they
can only focus on one striving each. E.g. Aphrodite knows nothing about cleverness or status,
none of the goddesses understand
justice. They rule their own domain and cannot be more: in this respect they are less,
they are partial humans. Zeus is the only one
who can take all their conations into account.
Together they are as good and as reasonable as we humans are. Or let us say it more precisely: as the human obeying them is. For if they are not absolute then they are relative. To us. Another way of saying this is that the gods are phenomena. They are not just what we obey, as a voice coming from outside, they are what we are, they are how we perceive the world and act accordingly. This thought is developed here.