There is precident for this in non-fiction. There has been internal strife in cultures through-out recorded history. Factions with-in factions. Look at the ancient Chinese Empire, Japan, The Roman Empire, Iran vs. Iraq, Etc, Etc, Etc....
The Factions unite temporarily against a common enemy, and when it is over, they beat on each other again for a while....
Soooo... I don't see a problem with this same theme in game.
There is precident in game for this. the Sith are constantly plotting against each other for personal gain.