The most sinister coup crowd I found has all the black non-pawn pieces conspiring against their own king, for a total of
12
regicide points. There are many ways to construct such a position, this seemed the most interesting:
EDIT: The question asks for a legal position, but in the comments OP indicated that an illegal position might be of interest too. Since I couldn't make a legal position with this idea, I decided to go completely overboard with the illegality, which allowed me to cram an extra piece into @Albert.Lang's brilliant discovery:
The basic idea is, of course, that if black could somehow have just one more non-knight piece, then replacing the c2 pawn with a black bishop would remove the lethal move from the white king, creating a need for yet another blocking piece at d2 or b4.