Can I tile over corian in my shower? The previous owners replaced all the tile in the bathroom with corian, even inside the shower. The corian is glued on solid, so rather than pull it off and very possibly ruining the sheetrock behind it, can I tile over it?

Are you talking about Corian tiles or sheets? That should not be sheetrock behind the tile unless this is a very old house. Greenboard and then later Hardiebacker and Wonderboard have been used for many years. I'd pop the old stuff off, you might even have difficulty getting yoiur shower valve escutcheon to fit let alone the handle.