My last flight surgeon (before I got out of the Army) got the authorization from the FAA to conduct up to a 2nd Class medical. It only involved him doing a little bit of paperwork for the FAA.

I scheduled the 2nd class with him at the same time as my Army flight physical, and he gave me both an upslip and a 2nd class at the same time. I don't know what it would have taken for him to do a 1st class.