Can styrofoam be used between plywood to bring up floor height
That will work as long as you use the dense form of foam board. The white board typically does not have enough compressive strength, at least to my knowledge. The blue or pink colored versions have enough compressive strength withstand the pressure. I have had 2 different occasions to do this type of install. One install was 4" of blue foam with woven wire mesh and radiant floor heat with 3" of concrete first and 2" of bluestone and setting bed over it. The other was 2" of blue foam over a concrete slab, with a layer of 2'X2' squares of OSB with plastic dimple board as a floating floor over the foam. These where done 10 years ago and still holding up fine, so yours should do well.

For your install, plywood will work fine. Use T&amp;G and screw through the foam and the into original floor to keep the large sheets flat. Every 8" on the edges and 12" in the center. This will also help eliminate the hollow sound and feel the floor will have over the foam.