The point here is that the law is actually quite vague.
Statements like the one from 777Contrail
You may not depart on a flight, or flight pairing, while you know you'll be outside of FDP AND having the means at your disposal NOT to exceed FDP (home base have standby/replacement crew).
is just plain wrong.
Although I completely agree with Champagne Lover
Now surely, when debating extension of FDP you should look at where the authorities were thinking when they drew up the rules?? There is a huge difference between operating a long-haul jet halfway across the world, with the chance of a diversion due to X, and then re-fuelling same day and getting the last stretch to out-base completed. Compare this with operating 4/5/or 6 legs locally and using the CARS loopholes for commercial reasons, where you should be employing sufficient crew to do the business you're involved in for your financial gain????
this is of no relevance.
According to the law, you cannot plan to exceed when setting out the pairing/string/flight. Anything after that (on the day of operations), passes the buck to the Captain who may utilise his legal discretion to extend the FDP for himself and his crew.
As the Captain, you have the responsibility for the safety of the a/c, crew and passengers/cargo. If you are worth four stripes, you will know when to exercise your discretion to extend and when not. The law leaves this completely up to you - as it should.