How far are you willing to go? Someone else may have a better idea, but I once reduced the sound between an office and a bathroom in a nursing home. This was done by removing the drywall and installing sheets of Cellotex, AKA Beaverboard, then reinstalling drywall over the top of it. This will create a problem for any windows and doors in the wall that you have, extention jambs will have to be installed. Pieces of cellotex were cut to fit in between the studs as well as sheets hung over the studs in the same manner as you would drywall, then hanging drywall over the top of the cellotex. Some people have used cellotex as a wall board. I don't recomend this, Cellotex doesn't have the rigidity or the strength to be used for that purpose.