It is. Unlike the ticket, the PNR is unique to each airline and controlled by each airline -- for their own flight. FF # is stored on the PNR, not on the ticket.

Even within the same alliance, different airlines can have a different FF # on it simultaneously.

The only time this may become a problem is at check-in. If the first airline also checks you in for the second airline flight, the FF # on the second airline flight may not be saved, so you may want to go and recheck-in with CI or have them add the FF # and reprint your boarding pass before boarding the connecting flight.