A number of people have mentioned Jesuit universities. I think you will find the Jesuit schools to be less strictly Catholic than Notre Dame.
Probably too late for the OP, but for others seeking a Catholic school, St. Anselm in New Hampshire might fit the bill. It’s a Benedictine college that takes faith very seriously.
DD2016 is at Marquette, we are not Catholic. Marquette is not overtly Catholic. In fact in recent years some have complained it is not catholic enough. She also looked seriously at Duquesne…it felt very Catholic. Her HS BFF goes to University of Dallas, she is Catholic, she says it feels so on campus