To me, there are a few ways the next round of expansion could go. The SEC and B1G could both end up with 20 schools or one could end up with 18 while the other has 20. Let's discuss the latter scenario.
If the SEC and B1G both expand to 20, the B12 would likely follow suit. That means there would be ten schools currently not in one of those those three conferences who would be getting in with full membership (football included). To me, the top nine candidates are pretty clear. In some order, the top nine would be UVA, Va Tech, UNC, NC St, Clemson, FSU, Miami, GA Tech, and Duke. The first four are premier schools in states the three conferences don't have a presence in. Clemson and FSU are football powers (less so recently for FSU, but they're in Florida and huge). Miami brings football history, a large market, and football history. There's a gap after that, but GA Tech (Atlanta market, excellent academics, some sports history) and Duke (elite basketball, elite academics, decent football) would be 8 and 9, in some order.
Who would get the tenth and final spot? To me, UConn would be a solid candidate, if they can continue- and build on- their newfound winning ways on the football field. However, there's a potential twist: Notre Dame- but not in the way you might think. The Irish won't give up their football independence so they won't take the last spot, but they still need a place to park their other sports. With the ACC losing its top nine schools, would the Irish want to remain in that conference as a non-football member or would they look to go elsewhere? On one hand, they may like the idea of staying in a conference with schools similar to them like Stanford, Pitt, Syracuse, and BC, but there's no doubt that the newly-raided ACC would be a step below the other three conferences athletically. In fact, that version of the ACC might even be in jeopardy of losing power conference status.
So where would Notre Dame go? They're not a good fit in the SEC. The B1G likely won't take them unless they join in football too, which Notre Dame won't agree to. That leaves the B12. The B12 would happily accept Notre Dame as a non-football member, provided Notre Dame plays a certain number of games per year against conference members, similar to the Irish's current agreement with the ACC.
But would Notre Dame have any other conditions for joining the B12? My concern is that they may use their influence to help Stanford land the 20th and final spot in the B12, by conditoning their agreement to join the B12 as a non-football member on the Cardinal being offered full membership. When the PAC fell apart, Notre Dame led the charge for Stanford and Cal to get into the ACC. Their ties with Stanford are stronger as the schools are similar in profile and play a head-to-head football game on an annual basis. Would Notre Dame use its influence and cache to help Stanford once again? On one hand, they wouldn't have a ton of leverage because the B12 would clearly be the next-best conference besides the SEC and B1G, so if ND doesn't get into the B12, where would they go? A vastly dimished ACC probably wouldn't be ideal. On the other hand, the B12 would benefit greatly from having Notre Dame in the conference, espeically with the SEC and B12 increasingly putting distance between themselves and the rest of the pack.
All of this is why I am concerned that Notre Dame may end up costing UConn a spot in the B12.