One small clue we have is that according to FXS, Secret Societies will require either R+F or GS. Since GS already has R+F mechanics, we can deduce it will deal with R+F mechanics. Maybe not entirely, but it will use them. So loyalty, governors, ages, etc. So I could see things like being able to install a governor in another civ, a la Ottomans. Maybe he/she will decrease loyalty in enemy cities, or act as a spy where you have full visibility over what is going on in the city. Or even if you don't install them yourself, maybe the enemy governor is a part of your secret society and thus has more loyalty towards you then their own native civ.