I'd be pretty shocked if the other team was anyone but VCU. They were already a target with UD before and as others have mentioned
SLU seems more likely destined to join the BE if they ever go to 11 or the MVC.
14 is a great number for basketball. It will allow the American to go to a 20 game conference schedule. You'd play 7 teams twice for 14 games and the other 6 teams once. Likely this would be done with divisions of 7 and one cross-division "rival." In theory, you could even make these divisions mini-conferences for non-football/basketball sports to cut down on travel expenses.
East: UConn, UCF, USF, ECU,
Temple, VCU, Dayton
West: Cinci, Memphis, Houston, SMU, Tulsa, Tulane, Wichita St.
So for example in basketball you could have UD/UC be the cross-division rivalry in hoops.
*Side note: I'm a huge college baseball fan (you have to be if you live where I live) and the American is a very good baseball conference. They have at least 6 teams with top-50 RPIs at the moment.