It also leads to the concept of layered alllegience or layered service in character creation... like doing an Army character with a term of Homeworld Army, terms of Subsector or Sector, anf then some Imperial terms, which sounds interesting to try.
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It might also be remembered that "lawered alleigiance" though it can cause strain, can also be mutually reinforcing.
A classic case is the British Regimental system(which by the way is copied in the Unified Armies of the Imperium-or is that United Armies?-no matter).
Anyway each regiment is not merely a administrative organization, but a tribe or fraternity with it's own traditions, such as holidays, strange ceremonies and feuds, or friendships with other regiments. Each regiment is nominally connected to a given region so that both local and regimental patriotism are combined with national patriotism. In former times and to some degree to this day I suppose, the officers were made up of people who had all been to the same sort of posh schools, schools that had policies that tended to encourage a tremendous degree of group loyalty on the attendees(They had a negative affect though; they were hard on those that didn't fit in. Sometimes the result was harmless or even positive, and created an "eccentric" who might actually benefit Britain. Sometimes though it created someone like Kim Philby).
Anyway all these national loyalties, regimental loyalties, local loyalties, and class loyalties combined to make an army with tremendous cohesion. In addition it made colonial units better-all the British had to do was copy the system in vassals, and they got very good results because though colonials might be indifferent to Britain they were loyal to there regiment and the reputation of their particular region.
The point of all this is that the "layered loyalties" are often mutually reinforcing. When there comes a time when such loyalties seem to be mutually exclusive instability will set in. An empire that can prevent that is likly to be successful. In fact I suspect that the 3I has psychologists and simmilar people assigned to make sure the "layered loyalties" work to it's advantage. And of course the nobility who had been bred for their whole lives in this system would know instinctively how to make it work-perhaps better than the shrinks.