I wouldn't say it could intensify another intensifier like that ("quite much" isn't correct, in my opinion), but you can use it with other adverbs: She dances quite well. He runs quite fast. I've run out of food quite quickly this winter. The seed is quite evenly spread across the field. Going back to your example sentence, a common alternative would be "quite a bit" or "quite a lot": She runs quite a bit. She likes it quite a lot. The verb "suit" would normally pair with "well": It suits her quite well.

It suits her quite well. Or "it suits her nicely."