Depends onthe operation.

61.51(e)(1)(iii) allows a pilot to log PIC time "When the pilot ...acts as pilot in command of an aircraft for which more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is conducted..." In addition, an ATP may log PIC time any time acting in command of a flight operation that requires an ATP under 61.51(3)(2)

So the "real" PIC can always log PIC time when he or she is in command of a required multi-pilot crew, whether the requirement for more than only pilot is because of aircraft certification or regulatory operational requirements (including OpSpecs that require 2-pilot crews).

Fortunately that's going to cover the PIC most typical 135 and all 121 operations. There are a number that can fall between regulatory cracks. For example, a Part 135 cargo flight in a single-pilot-certified aircraft without an OpSpec that requires (not authorizes, requires) a second pilot. In those situations, at least in theory, the only pilot authorized by the regs to log anything is the pilot who is doing the flying.

Seems silly, but remember that this is the same reg that allows more than one pilot to log PIC at a time.