Do not demolish the entire basement, but only as deep as not to disturb a new building.
Fill the basement and compact it layer by layer.
Don't demolish the entire basement, just dig deep enough that it doesn't interfere with a new building.
Fill up the basement and compact it in layers.
Completely different question than the basement: Have you already checked how the houses are connected? Very often at that time, houses were not built "side by side" as they are today, i.e. statically independent, but rather like a single house, with a real common wall, etc. Tearing down one half of such a house would be interesting anyway.