I found this in the new ALPA FAR 117 guide:

Q-29. Is the concurrence of the PIC necessary if a FDP extension is required for another flightcrew member, and could the PIC concur to an extension less than 2 hours?

A-29. The PIC must concur in all FDP extensions over 30 minutes even if it is for another flightcrew member. The PIC can also concur to only a shorter extension that he/she believes can safely be carried out even though the certificate holder wants a full 2-hour extension. The certificate holder must
keep a record of the PIC’s concurrence.


Q-30. If the PIC concurs with the carrier for a 2-hour FDP extension, can the FO refuse the extension?

A-30. Yes. Each individual flightcrew member must “sign off” that they are fit to fly before each segment, i.e., the PIC can accept a 2-hour extension but the FO can independently state he/she is not fit for further duty and could not under the circumstances accept the extension.


I hope this helps.