Plato and Freud’s concepts respectively of the soul and the psyche can be compared. That is a good question. Each has three distinct parts; appetite spirit and reason versus id ego and superego. Each has an etymology from psyche in Greek.
Plato’s troika is eternal while Freud’s is process. Neither has a purely material or physical existence although they occur in the matter of the brain. Each appear to be a way of classifying characteristics of human experience that today might be explained away through entirely material processes, yet one might also explain away matter through quantum phenomena like the Higgs field as well leaving nothing besides spirit at the heart of anything (in a sense like that of Leibnitz and his one-dimension spiritual monads could be taken as representative of a member of a set of theoretical spiritual structures sustaining energy).