I've seen it done. You need to have a general contractor or engineer look at it. The issues with digging the basement deeper is how does it affect the foundation/footers.
If money is not object, there is another technique....raise the house. Saw that done here once. House was on a crawl space....maybe 3 feet. They raised the house up, dug out some, and put a whole new "first floor" under the existing house. $$$$$