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https://thespun.com/college-football/big-ten-has-reportedly-vetted-10-schools-for-possible-expansion

There are 10 teams that have been vetted by the Big Ten for possible membership.

Those 10 schools are Cal, Stanford, Oregon, Washington, Georgia Tech, Virginia, North Carolina, Duke, Utah, and Miami

I am actually surprised that Colorado, Ariz, Ariz St, Kansas, Florida St, and Clemson were not on that list. I mean If Utah was included,  what sets Utah apart?

If we are going to 20 (not that I want to, just for discussion) and we are working from the list provided by @LittlePig then I think we should take these four schools:

Stanford:
Great research, #9 nationally.  Great athletics overall.  Their football and basketball have been shaky lately but they perennially win that Athletic Director's Cup for winning at a LOT of sports.  Gets us into Northern California.  

Washington:
Great research, #5 nationally.  Better overall historic athletics than any other available western school.  Flagship school in a reasonably populous state (Washington is up to #13 nationally with 7.7M people and grew by double-digits between 2010-2020).  

North Carolina:
Great research, #13 nationally.  Decent football history and an absolute blueblood in BB.  Flagship school in a populous (#9 and growing rapidly) state.  

Virginia:
Good research (#48), not terrible FB history and great BB history.  Flagship school in a populous (#12 and growing rapidly) state.  

Then we'd have to go to pods of five where in football each year you play the other four teams in your pod and all five (on a rotating basis) from one of the other three pods.  

My proposed pods:
East:

• Rutgers
• Penn State
• Maryland
• Virginia
• North Carolina

Great Lakes:

• Ohio State
• Michigan
• Michigan State
• Indiana
• Purdue

Great Plains:

• Illinois
• Northwestern
• Wisconsin
• Minnesota
• Iowa

West:

• USC
• UCLA
• Stanford
• Washington
• Nebraska

For BB I'd propose going to a 23-game league schedule made up of:

• Playing the other four teams in your pod twice each (8 games)
• Playing the other 15 teams once each (15 games, 23 total).  

If possible I'd balance the schedule by adding a tournament where the 10 teams playing 12H/11A games play on the road and the 10 teams playing 11H/12A host.  


New B1G Basketball Tournament Schedule:
Tuesday:

• The worst eight teams in the league play to get down to 16.  

Wednesday:

• The four Tuesday winners play the next four worst teams to get down to 12.  

Thursday:

• The four Wednesday winners play the four best non-pod-Champions to get down to eight teams.  

Friday:

• The four Thursday winners play the four pod Champions to get down to four teams.  

Saturday:

• Two semi-finals to get down to two teams.  

Sunday:

• Championship Game

I still don't understand why research spending has any impact on an athletic conference.

$$$$

This isn't really an athletic conference. It is a Content Generator (formerly TV network) and a research consortium. 

Athletic content generates a lot of money but academic research generates a LOT more. 

Sure, I understand that, fine, but how does adding say Washington's research budget help Ohio State?

Academic research doesn't generate any TV ratings.  Most of the grant money is Federal.  You apply for a grant and hope you get some NSF or NIH money.  Who your football team plays is irrelevant.

But they operate as a research consortium so partnering with #3 Washington is better for Ohio State than partnering with #106 Notre Dame.

How do they partner?  I don't understand that.  Some Washington professor applies for an NIH grant.  Why would some OSU professor know anything about it?

I don't know all the details but the analogy I always think of is having a neighbor that you borrow/lend tools with. I have a lot of tools. The ideal tool borrowing/lending neighbor for me is a Wolverine who has even more tools than I do. However a neighbor who was a Turtle who had somewhat less tools than me would still be a helpful partner. What wouldn't help me at all is if my neighbor was a Leprechaun who didn't own any tools at all.

Maybe that analogy is completely wrong but it is my shot at it.

How do they partner?  I don't understand that.  Some Washington professor applies for an NIH grant.  Why would some OSU professor know anything about it?

The high-dollar research schools are doing exciting, expensive, new-frontier type of research which costs and yields billions of dollars. 
The low-dollar research schools aren't. 
.
You want to partner up with schools on your level or above, not the one drooling in the corner.

so, if we're going on research spending, these guys are out

#41, $679M, Purdue
#45, $644M, Rutgers
#47, $625M, Utah
#48, $611M, Virginia
#50, $554M, Iowa
#75, $376M, Miami
#87, $307M, Nebraska
#149, $139M, Oregon