It defines both of our football programs (I went to Ohio State from 2004 to 2009). It is everything.
I think they should just leave the conference alone. We've had 11 teams for years now and we only had one division. Every team gets 8 divisional games. Instead of playing 8 out of 10 division peers each year, teams will now play 8 out of 11. Simply add in Nebraska and leave it alone. Make sure the big rivalries play every year and go from there.
I hate the 6 and 6 "Title Game" setups anyway. Teams should not play twice a year in College Football, unless by some freak circumstances two non-conference opponents play early in the season, go undefeated from there and meet again in the National Title game (or another bowl, for that matter).
Think about this: If the Big Ten had 12 teams in 2006 when "The Game of the Century" was played in Columbus, that game would have lost most of it's meaning, assuming OSU and Michigan were in opposite conferences. OSU beats Michigan and then faces Michigan on a neutral site the next week? Terrible. Just terrible.
It's perfect that our seasons always end up against each other. If OSU is undefeated and heading to a title game, they have to get through the Wolverines. If the Wolverines are undefeated and heading for the title game (Sadly, a long shot these days) they have to go through the Buckeyes.
That is the way it should always be.