I did this the other night. I used the Greatjon to win my trial by combat and I was heartbroken to see him kill Ser Barristan Selmy. I subsequently returned home, married Robb to Margaery, and formed a faction for Stannis. I declared war with the Riverlands and the Reach at my side. I had hoped for the Stormlands, but Renly rallied for Joffrey like an idiot. Naturally so did Tywin and Balon Greyjoy decided to be an ass and join him as well.

I put Stannis on the Iron Throne easily enough in the end. I made an executive decision to change Stannis back to The Seven since I didn't see this set of events really pushing him hard into the Rh'lorr camp - I preferred to see how he handled the realm without that huge religion modifier damaging his popularity. Surprisingly he ruled the realm fairly well. Jaime was stripped of his cloak and succeeded Tywin, who died during the war. Robb and Margaery ran off to become sellswords, where Margaery proceeded to pop out Daario's bastard and call him my grandson. I married Sansa to Gendry (in my game files, I have him as an acknowledged bastard) since in my playthrough, I decided Ned would have picked him up from Tobho Mott's shop like he promised Robert he would. I don't recall who I married the rest of the kids off to, but Catelyn gave Eddard another son.

Edmure tried to go independent immediately after Stannis won (despite fighting to put him on the throne), so I had to put my dumbass brother-in-law down while subsequently rescuing him from prison before Stannis destroyed the Tully line. Jaime tried to go independent as well, but he was taken down. Aegon invaded during all these wars, but he got his ass handed to him. I investigated the legitimacy of Robb's son and sent ravens to all the realm about him being a bastard, but that was not enough to remove him from the succession. Mance also tried to take the Wall, but me and Mace Tyrell showed him what for.

I had a few false starts where the Kingsguard kept killing my champions, as well as Eddard Stark himself. I'm not sure how exactly you would manage to do much of anything without calling on a champion. (I find myself wishing that in the books that Eddard had demanded a trial by combat - and picked Barristan as his champion. As the King's Regent, he would have that right.)