I like the Empire being one culture, in fact I think they are missing more elements of commonality. For example: which is the capital of the Empire? Which of the three factions is holding it? Surely this would be hugely important symbol-wise, and the holder would be in some ways the "legitimate" emperor at the beginning of the game. If it changes hands, the holder can claim to be the legitimate Emperor instead.
What they could do for differentiation is maybe separate troops a bit, like add 1-2 distinct units, especially towards the higher tiers.