Research: googled "concierge doctor", "private doctor", "personal doctor", "doctor to order", "medicine to order", "black market doctor", etc.
I'm writing a character who is terminally ill and wants to try a promising but experimental surgical treatment that may save his life. He can't get a hospital to do it because it's something new and untested (he's asked and they've refused, even though he's totally willing to be a guinea pig), so now he's trying to hire a private doctor, a clinic, or something of that sort to do it for him.
What he wants done isn't unethical or illegal (like, say, black market organ transplants) and doesn't require any special knowledge beyond regular medical/surgical knowledge, but it does require a doctor and surgical equipment and preferably access to a hospital in case something goes wrong. He has money, but isn't fabulously wealthy and doesn't have any shady or underworld connections. Basically he's an ordinary guy with his life savings in hand, who just needs to find someone or someplace that is willing to accept a patient coming in and going "here's what I want done, please do it for me", even if they don't have a referral and can't prove the treatment will help, as long as they're willing to pay.
How would he go about finding something like that given that you can't just Google "back alley surgeon" to find one? (At least my research on my character's behalf suggests that you can't.) What sort of places like that exist? Which ones might be reputable and not super shady or dangerous? I'm trying to go more for "private clinic with pleasant environment" than "back alley hack job" here.