The basement is more involved and you should consult a structural engineer. The slab frequently provides lateral support for the foundation walls and removing it can be very serious.
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Mid Jersey Inspections
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there are many companies that perform this service. This is actually a very involved process, with soil samples and tests. But, I think it is pretty painless nowadays.
The basment floor should be looked at by a good contractor, preferrably somone with an engineering background. Good luck.