Believe it or not, some buildings have been built that way, where they pour columns and deck using the soil as the "formwork", then dig out the soil underneath, and so on. Definitely do-able, but your existing concrete slab won't be sufficient to support the house with the open space you may envision. The concrete is not reinforced (likely) to span any distance so you need a structure in place that will support the concrete just as much as the house itself. Which will be challenging because your slabs probably have thickened areas where there are larger loads (slab edges, interior load bearing partitions, etc) meaning your slab is probably not a flat underside (imagine a waffle with the top side flat) which makes evenly supporting it tricky.
To do it, you'd need to trench underneath, place steel beams to support it, excavate, place your foundation and then put new structural support in. Not that I have done it or there isn't another, easier, cheaper and much simpler way. Just my thoughts.