Exclusion constraint with negated operator?

I wanted to create an exclusion constraint like

EXCLUDE (c1 WITH =, c2 with <>)

This gives an error:

operator <>(integer,integer) is not a member of operator family "integer_ops"

I can resolve that by using gist and the btree_gist extension.

My question is can I somehow express something like

EXCLUDE (c1 WITH =, c2 with NOT =)

It seems that's not possible at the moment. But is there any obstacle in principle or is it just not implemented?

We have a ton of overlap operators (geometric, ranges, arrays) but none for the opposite. Sometimes that's useful for exclusion constraints.

Thanks,

Torsten