Depends on the type certificate of the airplane and the restrictions of the PIC's type rating. I don't know about the Eclipse, but the CJ2 requires two pilots unless the PIC has the specific single pilot authorization. If the PIC is not single pilot authorized then you are good to go. If the PIC is, then you would need to be operating the aircraft under 135 where two pilots are required by the ops specs.
Frankly with your experience, 3 takeoffs and landings every 90 days in a light twin would probably keep them happy so long as you have some other flying going on.