is it possible for taxidermy to be redone/remounted?

I tried googling this and had many mixed results on the subject. Also, most of the results were about deer and I have a little cat.

This is Magic, she’s my cat that I had done about a year ago now. I love her but recently the shape of her head has been bothering me and I’m not sure what to do about it.

She was killed when a taxi basically ran over her head, so her skull was extremely damaged and I’m 99.9% sure that’s why the taxidermist had a bit of a hard time getting it right. I still love the result, but I would like to know if it would ever be possible for her to be redone in the future, and put on a new mount. Thank you!!