OP said "using a classic car chassis". I'm not particularly knowledgeable, but you can make a lot of modifications to an existing car, but building your own from the ground up would be mostly illegal. I think in some sense, the actual "car" is legally only the VIN plate or something like that. My state stop even doing safety inspections recently, and before that they were already pretty minimal; it was mostly a check that your lights and horn worked and that you had at least one mirror.

I'm Polish and of course it's possible, in fact it's very straightforward for one-off vehicles that you don't intend to sell, it just has to have brakes, all required lights and mirrors, there are many hobbyist groups in Poland which build and register their own cars that they then drive in public roads just fine.

https://bip.gliwice.eu/pojazd-zbudowany-samodzielnie-sam