Raising living room floor using rigid foam
I have a second floor sunken living room that I would like to raise to the surrounding floor level. I am considering using rigid foam board to take up the space and hopefully reduce noise to the living space below. I would place plywood and flooring on top of the rigid foam. The supporting joists are adequate for the additional load.
Are there concerns or code issues with this approach? Would I be better off just taking up the space with 2Xs and adding sound attenuation on the underside?