The new CARs are very clear when it comes to PIC authority in regards unforeseen operational circumstances as is explained in 700.63(1).
"The authority to extend or reduce a flight duty period due to unforeseen operational circumstances rests solely with the pilot-in-command and not the air operator." - Advisory Circular (AC) No. 700-047
When considering unforeseen operational circumstances it is typical to allow the PIC, after consulting with all crew members, allow or not allow an extension to the maximum FDP. But the PIC can, at their discretion, also reduce a FDP or extend rest to ensure crew members' fatigue does not jeopardize the safe operation of the flight.
Remember, if the operational circumstance is foreseen the maximum FDP can not be extended.