There is a product called Extendo-Drain that will do what you want. Some high end tile retailers may carry it, not the big box stores, or you can get it on line at places like www.tiletools.com for under $8. It comes in several diameters and you get the right one by measuring the distance between the 2 mounting screws on the drain plate. It will raise the height from 1/4" to 1/2". Clean the existing tile real good and get rid of any and all soap reisdue, oils, etc so the modified thinset you use to set the new tile over the old will bond properly.

Tiling over wall tile is generally not done, it can lead to several problems including how to finish off exposed edges and it may affect the cover plate over the hot/cold handle.

Thanks for the tips!

You mentioned that while shower floors may be tiled over, it is more common to remove shower wall tiles before re-tiling. But, if you want to keep the existing shower floor and remove the existing wall tiles, how does one deal with the waterproof membrane behind the tiles, which is a necessary part of the shower pan that you don't want to damage? Isn't it likely to be irreversibly damaged when removing the wall tiles, defeating the goal of keeping the original shower pan intact? Is there some work around? Thanks.

Extend-O is poorly designed. Its diameter may be smaller than your drain opening. The package specifically tells you that Extendo is not meant to support weight on the drain strainer...you must pack grout underneath it.

In my case, I needed 2.75" hole centers on a standard drain opening of 4.5 inches. The Extendo diameter was only a bit larger than the screw centers, so it "floats" in the middle. Sure, it raises the strainer 1/4" but doesn't raise the lip of the drain itself.

So what keeps the grout you are supposed to pack under the raised strainer for support from just falling into the drain--sooner or later? This makes Extend-O about as useful as a 1" plug for a 2" hole.

The only solution I can think of is to cut my own 1/4" high ring of 4.5" PVC pipe. This will actually match the diameter of the opening, support the strainer, and provide a raised lip I can grout up against to keep the grout in place and out of the drain.

So then what good was the Extend-O? I end up having to make my own extender anyway. Just wasted time and money.