Well there seems to be a lot of people in favour of giving Byzantine the unique ability to adopt and modify another Civs religion. I must admit it is certainly an intriguing idea, although I have no idea of what it would take to code this in.
But I will try and apply this 'religious adoption' to a hypothetical Civ scenario so we can at least flesh out what this might look like in game.
So to try and closely follow the 'historical' religious history lets just say that you start Civ 5 as Byzantine. Your neighbour is Rome who allies with Jeruslaem, a nearby religious citystate (I know historically it was a Roman puppet state but that's the most accurate way I can think of doing this).
Rome soon starts the religion Catholicism and chooses the following 2 beliefs
1) Founder Belief: Tithes
2) Follower Belief: Cathedral
Shortly Rome is able to enhance its religion and picks the next 2 beliefs
3) Follower: Monasteries
3) Enhancer: Reliquary
Now Rome's religion spreads to Antioch first and converts some of your citizens. Antioch is one of your Byzantine cities but it is NOT your capital. Roman Catholicism continues to spread and finally reaches your capital Constantinople.
At this point in time you haven't reached the 200 faith required for the first Great Prophet so once your first citizen is converted to Catholicism you get a message giving you the choice to adopt Catholicism as your own new religion. If you click no, you can choose Catholicism later by reopening the religions tab and clicking a new found religion icon. If you have multiple available religions you can choose whatever religion you prefer from this option. As long as there is at least 1 religious follower in your Capital you can adopt that religion.
If you choose to adopt Catholicism, the next thing that happens is you get to choose the name and bonus belief of your new religion. So we choose Eastern Orthodoxy and for the bonus belief we take 'Pilgrimage'.
Obviously for Byzantine it’s good to have more founder beliefs as these will only benefit your civ. Now because Catholicism (the host religion) is already enhanced we cannot choose anymore beliefs outside of a Reformation belief as our religion is also enhanced. You also cannot adopt another civs Reformation belief.
So our Byzantine Religion of Eastern Orthodoxy is now a holy city at Constantinople (the majority of the population is converted once the religion starts) and the capital begins emitting religious pressure. So the beliefs of our religion are
1) Tithes
2) Cathedral
3) Monastery
4) Reliquary
5) Pilgrimage (bonus)
So now Rome will not get the benefit of Tithe from followers of Eastern Orthodoxy in Constantinople and Byzantine will get this income instead. However our other city Antioch is still following Roman Catholicism so the benefit of Tithe will go to Rome. Our first priority then is to spread our religion as fast as we can and convert as many cities as possible to snowball the increase in gold and faith from our 2 founder beliefs.
Note that if Roman Catholicism had reached our capital Constantinople and we started Eastern Orthodoxy BEFORE Catholicism had enhanced then we would only start with Tithes, Cathedrals and Pilgrimage (bonus). In this case we would still need to generate a Great Prophet to enhance our own religion.
Otherwise we could have started a religion first and chosen whatever beliefs that were available as per normal.
Balance Issues.
1) If you adopt an enhanced religion you save yourself the faith cost of 2 Great Prophets. That is a saving of 500 faith. I can't do more than speculate if that would be an unfair advantage to Byzantine. Remember it does come at a cost of choosing all your own beliefs.
2) Fireaxis would need to increase the numerical limit of religions for Byzantine and probably increase the number of beliefs available
3) How should the AI respond if we take and modify there religion, Roman Catholicism. Should that cause a negative diplomatic effect from Rome or should it be positive or neutral?
4) Can a Byzantine AI be programmed to make the choices above to adopt a religion in this manner?
What do people think of this? As others have previously mentioned we don't know if Fireaxis are still reading the forums and making balance changes but if the forums are active with positive discussions then we may have a chance of getting their attention.
For instance the last patch added special unique artefacts to the hidden sites unlocked by the Exploration Finisher policy. The forums had been full of suggestions for that feature and its quite possible the devs may have read some of our ideas on that.