Suppose an airliner flight is full with passengers and the airline staff realize afterwards that there are employees who the airline wants to send to their shifts using that flight.

The airline staff decides to ask for volunteers to surrender their seats in exchange for compensation, but they don't get enough volunteers to make room in passenger seats for their employees to take.

Would it be legal for the airline to instead have one or more of the employee-passengers take the flight as "extra crew" (assuming there is an extra seat to strap into in the crew areas)?