The primary cause of doubling in the M1Rifle is operator induced. In virtually all cases the rifle only doubles, and never more than that. The trigger is pulled very slowly, and the rifle held lightly against the shoulder; many times from a benchrest. When the rifle recoils it hits the shoulder and bounces back forward where the trigger finger is still around the trigger, firing it.
If it were the sear, would it stop at only one extra shot, or would it fire multiple shots?