How is CD worded / handled in Europe, Australia & North America I wonder???
There is no such thing as "Commander's Discretion" in my company in Oz. It is "Pilot Discretion" and it is up to the individual.
Unless ALL individual pilot operating crew members, regardless of rank, agree to extend into discretion then the aircraft will not be continuing. (Just to be clear...if ANY SINGLE ONE of the pilots does not feel "fit" to extend their duty into the discretionary period then its game over and time to head back to the hotel/home.
All in...or none in.
Safest way to go IMHO.
PG