Can we add a floor to our parents' single-family house?

Regarding the neighborhood, there are identical houses in the immediate vicinity

That is already a good sign - your parents should actually know whether they had a development plan back then, or built according to §34A.
If it is legally possible, I would also proceed as Yvonne wrote -> look for architects with experience in existing buildings (ask right at the beginning when which costs will be incurred!) and then they should bring in a structural engineer - architects usually have good connections to reliable structural engineers.