I have pushed back on several claims and got what I asked for,
91 Chevy conversion van, totaled in head on accident, got an additional $$ for my recent rebuild on front end (had receipts).
98 Yukon with trailer (one I mentioned in earlier post), got new stinger and medical paid.
84 Fiero totaled (my daughter was hit), I met with adjuster and showed them that the car was all original and complete, with custom wheels. Doubled the amount paid and got the car back. Daughter got a lawyer to help with medical, she got full medical paid, plus a nice amount extra (even after lawyer took his cut).
I have found that a rational calm response, not demanding anything but just some basic discussion pointing out additional items that were missed in determining claim amount works. I also indicated that I was not going to get an ambulance chaser lawyer, but just wanted a fair settlement.