Is there another way to say, "drive the point in further?" or belabor the point?"
Solution 1:
harp away at (someone or something) or harp on TFD idioms
To complain about or dwell upon someone or something repeatedly and to the point of tediousness.
As in:
The man makes an observation about the woman that is less than flattering, then harps on with further derogatory comments.
Solution 2:
“Add insult to injury”—commonly defined as making a bad situation worse.