So i have 4 characters atm. 2 on republic and 2 on the imperial side. I really like what they did with the legacy family tree, sorting your characters on siblings, enemies, allies etc.
So because it adds a little extra fun and thrill to my gameplay experience i'm creating little stories and personal releations between them in my head, while playing.
So getting to the point, slowly .. I thought it would be cool if they added stories to the game for each releation you can have with one of your other characters. For example; Smuggler and Bounty hunter - Rivals with an interesting background story. Or Sith and a Jedai, two brothers one on the dark side and one on the light. Create another story and some cool conflicts betwen them.
If you want to take it to a higher level you could also start connecting the story lines betwen more than 2 characters.
I feel that with a right approach several stories could entwine really cool. And in the end you'd have one final story.