St Thomas has been invited to join the Summit League. This conference is D-1 AA in most athletics and includes other schools such as Denver, NDSU, UND, SDSU, etc.
Summit League is actually D1 (not D1AA) in all athletics that they offer. There is just a Div 1, 2, 3, and NAIA. With the exception being football, which offers a D1 FCS (formerly 1AA). You are either Division 1, or you are not, in all sports. You cannot pick and choose which sports go to which level. The only exceptions ever made on that would be hockey, where a select few programs are D1 hockey and D2 all other sports.
St. Thomas is a football school more than any other sport, so I don’t buy that they voluntarily left to move up to D1 just to join the Summit League. The Summit League has no football affiliation. So yes, they have found a potential home for all their sports except for football. I don’t think the Missouri Valley Football Conference is going to offer an invitation to St. Thomas. That would be like the SEC offering a spot in their conference to the top D2 team in the country in their region. Have seen some speculation that St. Thomas could join the Pioneer League, which is a non-scholarship FCS Conference. I could certainly see that being a possibility. But their football team would not be competitive at the FCS level (outside of the Pioneer League) by being non-scholarship.