I think it would be awesome it there was some sort of personalized, dynamic story arc with members of your legacy as the protagonists. Each character's role will be based on their relationship with each other within the legacy tree. For example, two allied characters can team up against one of your characters in the opposite faction, with one character acting as a temporary companion to your main.
This would also open the possibility of some interesting interactions within characters who are married or other family members. Imagine the aforementioned example but now you have to fight your own son, sibling, or spouse!
Anyway, this is just a basic concept, discuss it if you like and feel free to offer your own ideas.