I'm in the community (mid-Atlantic) and practice both. I am a partner in my private anesthesia practice, and we have a lease agreement with the hospital, whereby they pay the group for my time in the ICU (the other intensivists are hospital-employed). I'll cover one of the units (6-12 patients per day) solo for 10 weeks out of the year, and am in the OR for the remainder of my clinical time. There is definitely an opportunity cost that must be paid for creating a gig like this, but I decided that is worth it for me.
Both the hospital and my group are hiring, if you're interested, so a similar hybrid position can be made.