Personally I think a good PoD - at least in terms of buying time and using the "I am a citizen of Rome" line of thought would be a Successful Majorian - if only because any victory there would require the assimilation and integration of the Foederati, and through that develop better solutions for immigration pressures (not that they'd be called that) in the long term.
Don't get me wrong, it isn't a magic bullet - but you've got time. Your next big contentions (at least from a European perspective, as there were other nationalities that could develop seperately) - are a "Roman" vs "Persian" idea. (Much like the Greek vs Persian) - or West vs East.
You'll probably, assuming good things and no disintegration, have a situation where again "I am a Gaul, but I am Roman", "I am a Greek but I am Roman", "I am a Frank but I am Roman". Etc.
As to the effects, this might be the effect of larger states but I imagine you'd have some more vast projects to improve certain situations, like the Netherlands Delta works (heck, the Netherlands themselves). If only for grandeur and sheer resource capacity.
I also think that you'd likely have much bigger wars, as anationalistic Empires are capable of wielding much larger armies. As a result, you need larger armies to oppose them. However, these armies are not guaranteed to scale 1:1, in fact, you may have a smaller percentage of the population in field armies, and garrisons combined - simply because there are fewer external borders to fight along.
Alternatively, you have a solution where the state actively breaks down nations, especially freshly conquered ones in favour of their preferred nation. I've discussed this with the idea of Janissaries before, but that idea could be applied in any period. It would be brutal, but you invade, capture the residents, settle the region with the soldiers that conquered it, distribute the captive residents in the far corners of the Empire and brainwash the kids.
So yeah, you've got a form of unified multiculturalism of a different era, or... state-built mono-cultures. Neither are exactly pretty.
(Nobody said that butterflying nationalism was prettier than nationalism).