I know that Aristotle and Plato play undeniably instrumental roles in recorded philosophy. However, I feel like Plato’s writings influenced Rome ever since they took Greece, mostly because Rome just absorbed everything and made it their own. No copyright laws in ancient conquest ;) Is it possible that the Roman Empire was the manifestation of Plato’s Republic? I know that he has split the state is symbolism to teach the tripartite soul, but was the Roman Empire have been that Republic? If so/not so, could you please expound on the historical contexts of application?
This very recent discussion, though not directly answering your question the way it's phrased, should give you the explanation you're looking for.
The bottom line is the apparent similarity of the Roman state to Greek political philosophy is an imposition of Greek political philosophers trying to use Greek political models to explain the Roman state, largely for the benefit of other Greeks.