If the remaining plug is loose in there... I've seen a guy (My Dad) use a shop vac with a reducer to suck snapped plugs out of the head sockets. And another guy (my grandfather) use the plugs that he did get out to size a section of rubber vacuum hose that just fit over it and slip a metal sleeve over that using a narrow pipe shorter than the hose slipped over it to push it down over the tip of the plug..then while holding the rubber hose push the pipe down to put a squeeze on the end then pull both out in one motion up and out...resulting with a plug stuck to the end of it.

If its nested in there then you'll need some kind of leverage to snap it then use the tool outlined by Nuke...jz and the others above.

Boom
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