The decision whether to have a basement or not is so essential that I personally wouldn’t just slap a basement underneath. It opens up entirely new possibilities.
In principle, yes.
This is now the prime example of why you should ideally factor in the topography of the plot from the start.
With a longitudinal/transverse elevation difference of 70/120 cm (about half of which is within the footprint), I saw no topographical indication (and there was no other concrete information) for a mandatory basement. Now I interpret the new information as meaning that the load-bearing soil probably only lies at the depth where you could also lay the floor slab if you were building a house with a basement. Analogous to a car accident damage, so to speak a "economic mandatory basement." However, first I see a significant difference between switching from pile foundation to a useful basement on one hand and the costs of the previous planning’s tonnages being hammered out (just for the back and forth of the stairs and downpipes, one could have planned an entire holiday bungalow with the same manpower!); and second I don’t see the effort of a redesign as worthwhile: practically, you "gain" here only the space of the building services room placed underground, the rest of the basement won’t really be used (with light well excavation for relocating a study the effort would be too great again), so in net effect there would only be a floor plan to "redistribute" with two decimeters less edge length.
But then we’d be right back at the exact point where the original poster soon continued to discuss alone! — so this wouldn’t be an opportunity. If the terrain allowed for a living basement and such was desired, the cards would be dealt differently — but that’s not the case. Besides: even in the thread at least the husband eventually did get around to typing himself, which unfortunately is not granted to us here.