I'm not sure what route we could see going further. Informally it'll always be a power game - does the Army back you? Does the Church? Does the Bureaucracy? Any two and you've won. I'm not sure what direction it could formalise towards. A stratocracy wouldn't be a vast deviation, but neither would a Bureaucratic Empire - D3 essentially rose as a Bureaucrat with support from the military.
I think it might end up essentially as a state defined by a mix of paternalistic conservative institutions - nothing free-wheeling, very stable, downright boring sometimes, but reliable institutions with the Emperor essentially only acting a Commander-In-Chief and Institutional Police. It might be that the Army is always essentially the primary institution, the one that HAS to be happy, but effectively any one could raise an Emperor, maybe even the Imperial Bank at some point, it'd all be a game of who can get the Army and maybe Treasury on side.
I think we're never seeing a non-Imperial Roman State, short of a revolution, and I don't see what it'd be built around if it did, but I do see the idea of the various institutions having their own candidates, and pushing them in corridor-politics, with it only being dangerous if the Army isn't pleased, or if the Army is completely divided.
It sounds to me like you're somewhat describing the West European estate system. With the first second and third estate being the Nobles the clergy and the commons. Except in this case rather than three you've added a 4th in the form of the bureaucracy. However i don't think it particularly matters since dynatoi have been so broken and replaced with a gentry system ala England but sans a parliament.