Multiple event trigger and actuation system

A multiple event trigger and actuation system including an actuator having an actuation component, a frangible dome and a pressure shiftable sleeve, a trigger having an incrementally movable stem, a holding configuration operably connected to the stem and configured to allow an incremental movement at a time based upon a pressure cycle and then hold the stem in such incremented position, and a rupture disk, the disk being positioned between a port to a pressure source and a trigger chamber, and a trigger transfer sleeve operatively connected to the shiftable sleeve to cause movement of the shiftable sleeve upon movement of the trigger transfer sleeve.