They can't exactly occupy the same space due to the Pauli exclusion principle. IIRC that's believed to be the final "barrier" that prevents neutron stars from collapsing into black holes. But this is also getting into the tricky parts of wave particle duality, so the precise details are a bit difficult for me too.
Only cats can violate Pauli's principle. Anybody who had a cat can attest to the fact they can go through walls. Just close a room with a cat inside and - given enough time - the cat will escape.