Considering the game's focus on cultural intermixing, it would be pretty neat if you were able to acquire some bonuses from other cultures/players either through conquest or with strong alliances. Obviously this could get very overpowered, so maybe you're only able to acquire one extra bonus every era and you also have to give up one of your other bonuses. 

This could be hard to balance, but it would add a whole new layer to the game, and it would also be quite historically accurate.

Could be interesting but indeed hard to balance

Could just be something really simple, upon conquering a city, this city unlock assimilation project which could give a boost empire wide according to the affinity/what the culture is best at in current game:

1. Agrarian: Bonus growth in every cities (2 turns or so)
2. Militaristic: gain 1 unit
3. Scientist: gain science progress toward a tech (that the culture knows if possible)
4. ...