The following definitely falls under the YMMV category, but it's worked for me twice...

As my complex (15 or 16 segment) held itinerary is about to expire, I call an AAgent and explain that I would like to cancel the itinerary and have the AAgent immediately rebook all segments in order to gain another two weeks to finalize my trip. (Yes, I understand that all my released flights may not go back into available inventory, but that's a risk I'm willing to take because the itinerary is about to expire anyway.)

Faced with rebooking such a complex itinerary, the AAgent cheerfully offered to extend the original booking by another two weeks.