My idea is to create 3 points on the map of Cyrodiil like cities, mines... where the three factions have to fight each other in a kind of battleground (for example 6vs6)...The factions which wins the most matches in a certain time will hold this point in Cyrodiil. Holding one of these point gives the faction some advantages like more alliance points or other stuff.
I think this would be a good way to integrate some additional kind of small scale pvp and variety into the Cyrodiil pvp and satisfy ppl which like to play battlegrounds.