Prefabricated house on a sandstone base

Hello,
I recently inherited an old half-timbered house. After various conversations with experienced craftsmen and a structural engineer, they no longer consider the half-timbered house "worth preserving," as it has been remodeled, extended, and repaired over decades with materials that only harm a half-timbered house, etc. Ultimately, we are leaning towards demolishing the house and maybe putting a prefabricated house on the sandstone base.
What is the opinion here in the forum: Is something like this possible? Pouring a slab on the sandstone base and then continuing with a prefabricated house? At least the beautiful sandstone cellar would be preserved that way.
Thank you very much for the responses

You determine the worthiness of preservation. Possibly, the refurbishment is not economical, but that is a different assessment.

In our neighborhood, exactly this idea was implemented. The sandstone cellar was completely preserved. It gives the house a special charm between modernity and this worthy-of-preservation old stock.

Hello, I have an old house with a sandstone wall, partly sandstone base.
There was also botched work done on my house.
My whole house, as it is nicely called, stands on "compressed clay."
So no real foundation. My house is located on a [BUNDESSTRASSE]. The passing trucks have, unfortunately, shaken it even deeper into the ground in recent years. Our basement, however, is dry.
If the foundation is load-bearing (ask a structural engineer) and the basement is dry, then why not? However, I regularly curse these "legacy issues"!
But I also like the charm of the old house.

Economy must not be the top priority in this case...

Hello , your question cannot be answered reliably in the forum on its own. We neither know the substance nor your new wishes. Generally, a lot can be done with old buildings...

A few houses down, there has been a timber-framed house on an old sandstone cellar for several years. Solid wood (was built by our general contractor) and stone on stone (someone here in the town does that) is also possible if the cellar is still in good condition. We decided on demolition and that was a good decision. It was actually always clear that the excavator would come. I grew up with my grandpa always saying, "Child, tear it down, old stays old." Since I like half-timbered houses, we had considered renovating. It would have been more expensive with many compromises. During demolition, surprises came to light that confirmed the decision. Just quickly checked near your place We live Haus, Albert Haus, Erhard GmbH, and Brandl Bau have built on old cellars. For the demolition, we had good experience with Leinweber.