They did something like that in AvP Extinction.
With Marines, there were bandits and different squads.
With Predators, yes, there were different clans, it made the fourth level particularily difficult.
With Aliens, there were the bright yellow ones that were created by humans and using DNA of an Alien. Of course, they went out of control, and they are another player in this large storyline.
I don't know if there are Jockeys or Pilots in the game, but maybe there's some background detail I missed.