I propose the following for a new Big East conference. As of 2015 there will be 12 football schools in addition to 9 basketball only schools.
Football: Cincinnati, Boise St., UConn, Houston, Louisville, Navy, Rutgers, SDSU, SMU, USF, Temple and UCF
Basketball Only: Georgetown, DePaul, Marquette, Notre Dame, Providence, Seton Hall, St. John;s, Villanova
If possible, invite the following A-10 schools to join the above listed basketball only schools: Butler, Dayton, UMass and Xavier
Then, with 12 teams on both lists, basketball schedules could be the other 11 teams in your division, and 5 of the other schools, for a total of 16 conference basketball games. In football it would likely be 8 football games on rotating basis year after year, and allow for 4 non-conference games.