There are, but the right answer is very specific to the problem at hand (client objectives, soils, access, headroom, budget, contractors, ...). Best to ask a civil engineer who can spend some time on your site and get a full picture. The alternatives might involve other materials which are not necessarily preferable to cement - eg steel micropiles, or expanding resin - and at least some cement concrete is likely to be used to tie the existing stone to the new foundation.

Eg if the objective is to fix stability problems with the existing wall, the answer might lie in drainage of the earth backfill, or retaining it another way. Whereas if the objective is to dig down to make the floor level lower, some form of new concrete foundation is likely to be needed.