This is an idea I had and I was wondering if anyone has ever done this.
You'd make a character and play him or her however you want like you usually would until you get to a significant choice. I'll use Dawnguard as an example. When you get to the point where you must take Serana to Harkon, make a new save when you enter Volkihar castle. Talk to Harkon and reject him. After he banishes you make another new save and then reload the first one. This time accept Harkon's offer and save over the first save. From here your character's story splits. You can play the same character, but explore two different outcomes to their story. You could also do this with the civil war.