Part 117 is strict — but not absolute. There are exactly three doors to a longer day, and each has a different trigger.
If something unplanned and unforecast appears before takeoff — weather, equipment malfunction, ATC delay the company could not reasonably expect — the PIC and the certificate holder together may extend the FDP (or the FDP + reserve-availability combination) by up to 2 hours. Conditions:
Once airborne, the PIC may extend as necessary to safely land at the next destination or alternate (§117.19(b), and §117.11(b) for flight time). No 2-hour ceiling — but again, extensions over 30 minutes only once per rest cycle, and the company reports them to the FAA within 10 days.
§117.5: if you report fatigued you cannot accept the assignment, and if you become fatigued mid-duty you cannot be forced to continue. A fatigue call ends the FDP; it never lengthens one. The company then must give you the required rest before anything else.
The once-per-cycle rule is the one crews cite in scheduling disputes: if you took a >30-minute extension Monday, you cannot take another until a 30-hour free-of-duty rest intervenes. The FAA report requirement (within 10 days, corrective action within 30) also creates a paper trail you can request through your union.
See both the scheduled and extended limits in the free Part 117 calculator.
Verified against eCFR 14 CFR 117.19, 117.11, 117.5, 117.29. Educational only.