US Gulfstreams . . .
Swiss Challengers
I would assume most, if not all, medical services offering flights, have access to larger aircraft. If not their own aircraft, any flight can be sub-contracted out.
As for staff required for flights, I'm unfamiliar with any legal requirements, but it appears from reading website info from medical flight operators - it is up to whomever is paying for the flight what services and staff are requested.
You can call toll free or email your question below;
Contact AirMD Air Ambulance Services
Toll-Free (800) 311-3412
AirMD Clearwater, Florida
info@airmd.net