Possibly create religions

I know it sucks to compare games in a scenario like this, because one doesn't want to copy.  But the religion in Civ V is actually really fun and engaging.  Creating/manipulating a religion is a fun aspect of the game, and push my religion on someone else (while I hate it IRL) I looooove doing in civ (Byzantines ftw).

But I think it would be a cool like aspect to make the game more dynamic.  Possibly each faction starts with their own base beliefs which are have benefits/drawbacks, but the big thing is these beliefs have some political parties who will like it, some who won't , and some who wont care.  So now, as your population becomes more diverse (unless you are Horatio #genesplice) you might need to make some changes to your religion (similar to laws) to make people happy.

Now, have a relgious political party in power could do multiple things.  It could amplify the effects of the religious deliefs, or it could provide more powerfull religious beliefs to choose from.

Now, this all seems very smiliar to just good old laws, but the difference would be that like culture, religion could spread.  Now, I'm still not certain how this could be differientiated from culture, but in essence, religion could creep into other empires' citizens, and action would need to be taken to shut it down (via infinite "inquisition" production) or even possibly embrace it.  Maybe this religion actually helps the population of this system! 

Diplomacy could then be affected by this.  Possibly if some religions overlap in beliefs, a faction will be more accepting and vice versa.

To me, it seems like adding religion would be right up this game's ally.  It loves providing as many ways as possibly to play the game and achieve your goals.  Heck, a religion victory could even be a thing.  Make sure that your religion in the only one in the galaxy, or something like that.