As a general rule if you can ensure the structural stability of the ceramic tile installation you can install anything else you want on top of the tile. Look for cracks in the grout or loose tiles to see if the area is stable. Check for hollow-sounding tiles by tapping on them with a wooden stick or the plastic end of a screwdriver to check. Loose tiles need to be replaced before you can install anything else on top of the tile.
Depending on the new material, you may not be able to install on top of tile based upon the adhesion requirements of the new product. Most ceramic tiles are covered in a slick glaze that other types of adhesion have an issue gripping. Epoxy-based or silicone-based adhesives can be used, but you should check with your new material’s manufacturer to see what kind of adhesive they require and whether or not you can use it with tile.
Laminate and hardwood floors that are not nailed and glued down to the installation surface can be put directly on top of tile without regard to adhesion. Known as floating floor installations, they are generally installed on top of a layer of padding that is simply rolled out over the top of the tile. The boards are then glued to each other but not to the floor, and installed over the surface of the tile. As long as the installation is flat and structurally sound, you can put floating floors on top of any tile.
While carpet can technically be installed on top of tile because it rests on top of padding, you have to worry about how to attach the tack strips to the edges of the room. Normally tack strips are nailed down on top of a wooden subfloor, but with tile, you can’t nail into the surface. Epoxy adhesives can help work around this, or you can buy special tack strips that are meant to be used with concrete and tile, although they cost more than normal strips.