The goal for expanding to 12 teams is the championship game, right?
Otherwise there isn't a need to add a team. Thus, the key point is to allow the championship game to be the most compelling game possible for most years. That means splitting up OSU and Michigan into different divisions to allow them to meet for the conference title. However, the Big Ten should follow the lead of the ACC and set designated rivalries across divisions.
Therefore, I think Michigan and OSU end up in different conferences but play each other EVERY YEAR as a designated rival.
I don't think the Big Ten would want to split Minnesota and Wisconsin into different divisions because maintaining that rivalry for a divisional title is pretty compelling.
The rest of the Big Ten is pretty much a crap shoot - other than Penn State and OSU.
Therefore, I could see the following split with the designated rival in parentheses.
Big Ten - Big Division
Michigan (Ohio State)
Michigan State (Wisconsin)
Indiana (Purdue)
Penn State (Pitt)
Iowa (Minnesota)
Northwestern
Big Ten - Ten Division
Ohio State (Michigan)
Pitt (Penn State)
Minnesota (Iowa)
Wisconsin (Wisconsin)
Illinois (Northwestern)
Purdue (Indiana)
That gives each Big Ten team six games against the same opponents each year. The Big Ten could then do the same rotation that the ACC has and play another two teams from the other division on a two-year back-to-back rotation schedule (i.e. in Year 1, Minnesota would play all of its divisional teams, Iowa (dedicated rivalry), and Michigan (home) and Indiana (away); in year 2, Minnesota would play all its divisional teams, Iowa, and Michigan (away) and Northwestern (home); year 3 would be all divisional teams, Iowa, and Northwestern (home) and Penn State (away).)
The payoff is that you create likely situations for big rivals to face each other for the Big 10 Championship. An Ohio State - Michigan Big Ten Championship would pull a huge TV number and would sell out any stadium within the geographic footprint. The SEC and ACC don't seem to care about having teams potentially play more than once - in fact, it adds a little something.