Heck, pretty much anything causes styrofoam to look like glop. Brake cleaner does an especially nice job of attacking it.
3M™ Spray Adhesive for StyrofoamŪ Brand Foam appears to be a nice exception. I tested a scrap piece of 1/4 inch sheeting with it, and this stuff did not eat the sheeting.
I was toying with the idea of using this spray along with 6 mil plastic wrapping for construction use, but the plastic did not really want to stick to the sheeting. It would stick, but it would also peel off the sheeting fairly easily.
I was also toying with the idea of using garage floor epoxy coating, but that stuff is expensive.