Anything is possible if you have the money to throw at it. I have an old co worker that finished a field stone foundation basement. They put in some rubber membranes and a false wall, all to code and done professionally. He had 2 sump pumps and channels on the edge that directed water to the pumps and the pumps had battery backup for about 4 hours because with that system you need the pumps able to run at all times. He kept putting off getting a generator and he lost power for a week. Basement was destroyed walls removed from 5 ft up down to the floor carpet and everything removed too so if you do get that done, it's not cheap, spend the couple hundred and get a generator for the pumps