Dual passport (EU, non-EU) and residence registration in Poland

I am a dual passport holder, one EU and one non EU. Can I register my residence with both of them in Poland.

No, you have to pick one and use that. By the way, if you go with the non-EU passport, you'll need to get a residency permit and a work permit.

So if I have already registered with the non EU passport can I register with the EU passport after the temporary residence card expires? Or can I cancel the none EU passport registration and register again.