This isn't an entirely new idea but I wanted to add to it. If you adopt an existing religion founded by another player you could choose to stay as a part of their church or separate, keeping all tenets they've acquired up to that point minus their most recently added one and add onto it from there. 


Possibly both sects would share half of the other sects followers towards gaining tenets to show how the broad idea of their religion has spread even if it's slightly different. Or even better the conversion of followers shared is determined by the tenets shared between them.


A new civic could involve whether you see these sects as valid interpretations of the faith giving you a larger percentage of their follower counts or heretical allowing you bonus pressure against them.