Well In a room I had before putting new carpet down I glued and screwed 3/4 MDf to the floor a screw every eight inches bothways. That ended all the bounce in the floor I started doing that before laying ceramic tile floors in different homes a tile layer I knew told to reinforce the floors that way so the tiles didn't nearly. So I carried that idea with me before I layed the carpet down in that stereo room. As others have pointed out it maybe worth your time to reinforce the floors from underneath. I would do the extra layer in the floor if you can get them to do it before they lay the rug. Personally if they haven't done the drywall I would have them use 5/8 fire rated it is much more dense. Those are just ideas if you get a chance to have it done before they finish the room. Really not too much money that way.
Regards