Some kind of cultural syncretism. Not just a 3 or even 4 tier system, but the option for wholly unrelated cultures to come together and semi-unite into a new or evolved type of world-view. The Turko-Persian-Arabic synthesis is a good example of this.
More granularity overall too. For this reason I'd prefer a 4 tier system over a 3 tier one. Even if many cultures, particularly European ones, might only benefit from a 3 tier system, others with vastly different lifestyles like Tuaregs vs Riffians are already far apart, and that's without even considering the difference between individual Tuareg tribes (sub cultures). So in this case it would be like Kel Ahaggar > Tuareg > Saharan Amazigh > Amazigh. For a place like England, an example might be Northumbrian > Anglo-saxon > West Germanic > Germanic.
But then there would also be hybrid cultures, preferably dynamic ones, like Midlander > English (Anglo-Norman) > West Germanic > Germanic, or
Arabo-Picard > Arabo-French > Gallo-Romance > Romance
At the same time, even with more granularity, different cultures shouldn't just automatically rebel, but they also shouldn't just openly accept syncretism either. At this point the mechanics would get too complex just for vanilla, but something simple like the amount of time a region has been independent or dependent, as well as autonomy, pastoral vs agricultural vs urbanized, and the above synthesis mechanics and prestige status would represent the cultures of the time extremely well.
This system could also create new cultures that didn't exist at first. A real life example of this would be Transylvanian Saxons (Franconians), being so separated and distant from their relatives they would just up as a new culture (Transylvanian Saxons).
Ok this is a little overboard but something simple with this in mind would be cool.