In removing the plastic part still there, piece broke again, this time it was the male part that's inserted in drilled hole in the wood (this tiny plastic male part supports entire weight) that broke, halfway into the hole.
Thus the remaining broken tip-end half is still there, wedged into the hole.
Gotta get it out of there, so we can insert a new but identical plastic support's male-part into the hole.
I volunteer to measure hole and plastic male part with dial caliper and get proper bit and drill new hole an inch away.
Answer: NO!, you'll make it ugly.
So, how to get that plastic piece out of the hole?