> Another professor […] once said that the single particle wave function is more fundamental than the multi-particle wave function. Nevermind […] his research […] where the molecular wave function can't be well approximated using a product of single particle wave functions

Depends on what you mean by "multi-particle wave function". The way it is usually understood (I think), it includes all possible tensor products of single-particle wave functions. Then it should be possible, shouldn't it?