Just so you can visualize what we would be talking about:

First BBB's suggestion:
Big 10:
Duke, Georgia Tech, Maryland, North Carolina, Virginia

Boston College, Ohio State, Penn State, Rutgers, Syracuse

Indiana, Michigan, Michigan State, Purdue, Wisconsin

Illinois, Iowa, Minnesota, Nebraska, Northwestern

SEC:

Auburn, Clemson, Florida, Georgia, N.C. State, Virginia Tech

Alabama, Florida State, Kentucky, Tennessee, South Carolina, Vanderbilt

Arkansas, Louisiana State, Mississippi, Mississippi State, Missouri, Texas A&M

Big 12:

Louisville, Miami, Pittsburgh, West Virignia

Kansas, Kansas State, Oklahoma, Oklahoma State

Baylor, Texas, T.C.U., Texas Tech

PAC:

Arizona, Arizona State, Colorado, Utah

California, Southern Cal, Stanford, U.C.L.A.

Oregon, Oregon State, Washington, Washington State

Or if the Big 10 and SEC both take 6 from the ACC in order to dissolve the conference and the PAC takes 8 from the Big 12 in order to dissolve the conference:

Big 10:
Duke, Maryland, North Carolina, Penn State, Virginia

Boston College, Notre Dame, Ohio State, Rutgers, Syracuse

Indiana, Michigan, Michigan State, Purdue, Wisconsin

Illinois, Iowa, Minnesota, Nebraska, Northwestern

SEC:
Auburn, Clemson, Florida, Georgia, Georgia Tech

Alabama, Florida State, Mississippi State, South Carolina, Vanderbilt

Kentucky, N.C. State, Pittsburgh, Tennessee, Virginia Tech

Arkansas, Louisiana State, Mississippi, Missouri, Texas A&M

PAC:
Iowa State, Kansas, Kansas State, Oklahoma, Oklahoma State

Baylor, Colorado, Texas, Texas Tech, Utah

Arizona, Arizona State, California, California Los Angeles, Southern Cal

Oregon, Oregon State, Stanford, Washington, Washington State

Out from the ACC: Louisville, Miami, Wake Forest
Out from the Big 12: Texas Christian, West Virginia
Independent Out: Brigham Young

This would probably require ESPN landing the Big 10 T1 contract (to put them in the mood to relinquish ACC property to the Big 10) and for the to acquire a nice piece of the PACN (for them to put Texas, OU, and Kansas in the PAC).

Now those were the suggestions and they are nice and neat but they require a lot of things to break right for the Mouse.