The key to the answer will be found in the airline's Operations Manual Part A. Below is a typical example (taken from a UK airline Part A)
Unpressurised Flight
Unpressurised flight without passengers, up to a cabin altitude of 10,000 feet does
not require special authorisation. All other premeditated unpressurised flights require
authorisation from the Fleet Office and must comply with the following conditions:
1) Passenger flights, if authorised, will not be operated at a cabin altitude
exceeding 10,000 feet
2) Non-passenger flights may be authorised above 10,000 feet but not above
14,000 feet cabin altitude provided there is sufficient oxygen and heating
equipment for all crew members for the duration of flight above 10,000 feet.
3) Flight above a cabin altitude of 14,000 feet (excluding test flights), is not
permitted.
If a defect occurs after take-off which renders the aeroplane unfit for pressurised
flight, continued flight to destination will be at the discretion of the commander who
will consider the implications of reduced range, terrain clearance, weather and icing
associated with low level cruise. The cabin altitude restrictions above will be
observed.
YS