Hospitals make the lions share of the profits. Non-corporate hospital owners are famously poor managers and tend to spend the money not wisely until they go bankrupt, then a corporate system buys the hospital, restructures, and takes all the profit. See HCA, Tenet, Partners, Mayo, Stanford, Anthem, etc. Fun fact, HCA was cofounded by Bill Frist's father. Bill Frist became a cardiac surgeon, then a US senator for Tennessee. At one point he built another healtchare system and sold it to Anthem.

You'd think the medical schools might remain independent under their universities, but that often turns out to not be the case as well. Turns out asking for handouts from the endowment looks a lot like bankruptcy, and the rest of the university takes a dim view of it, especially considering how home addresses of their physician colleagues (hint: very large houses in the best neighborhoods). See Tulane, Georgetown, etc. The state school systems, like the UCs, tend to do better, or are at least shielded by the state budget.

If you point to Mayo, Stanford, and Partners as exceptions, I'd say they're the exceptions that prove the rule. Mayo has always been a self-sustaining business. Stanford and Partners have ready consultation with the strongest business schools in the US, if not the world, and the endowments to match.