Well - crazy as it sounds, I had something similar. When I was younger, I bought this house in Minnesota. It had been a one room school house. The basement, such as it was, had been hand dug. Some walls were poured, but others were mortar troweled over dirt. It was my first house and I didn't understand what i had bought.
I expanded the basement somewhat. I used house jacks and timbers for temporary support. Then I broke the concrete, dug out the earth and put in blocks. I hauled many buckets of earth from the basement. I've wondered to this day whether the neighbors thought I was burying a body down there. It was a man-hour intensive use of my time. I did not do the entire basement. Perhaps, you could do something similar and only replace the bad sections of concrete.
If you lift the entire house, you may get cracks in old plaster and other problems. Sewers, wiring, plumbing, etc will need isolation disconnection. Green field construction is often preferred to Brown Field.
Would I do it again? No. If I had to do it again, I would have shopped around and found a house with a decent basement and foundation. In addition, my time would have been better spent with other activities.
If I had spent that time learning about finance and money instead of digging in the basement years ago, well,......