Help with counter top decision

I have purchased a summer cottage with a dated counter top. The cupboards are home made and impressive however the counter top is made of a brick color porous(sp) tile whose grout has seen it's day. My wife is totally grossed out by what may have seeped into the tile during food prep and wants to replace the counter top with 12x12 granite tiles left over from another job. I see no way of removing the current counter top without tearing the cupboard framing up. 3/4 plywood with hundreds of screws topside into the framing.
Is it possible to screw down 3/4 plywood onto the current counter top (through the current tile / plywood and into the cabint structure) and tile over? The current structure is solid and level OR am I better off chiping the current tile off, hacking away at the morter bed to get a level surface OR getting at the screws to remove the plywood and start anew? I appreciate any and all advice.
Thanks
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jim wrote:

A BFH should make short work of the existing tile. Usually, once you get a corner started, it comes right up. Smoothing will be a problem- a 5-inch masons chisel and 3 lb. hammer are what I used as a kid to clean forms with. That should get it smooth enough for backer board (not plywood)or a new mudbed. Drilling through the existing tile will likely shatter it anyway, not to mention making for a bizarrely thick counter surface.
Or you could just try tiling right over the existing tile, using it as the substrate, assuming you can think up a way to trim the edges to get it acceptable looking. (Maybe whack off the edge tiles and use a wide hardwood strip?) If it is as solid as you say, it should work as well as backer board. Dry-lay a few rows of the granite, and put a level across them. If the fluctuations are minor, thinset should allow a level final surface. You WILL need to heavily degrease the old tile to get a good bond, maybe even do a wash with brick acid.
I suppose telling the wife to get over her germ phobia is out of the question, SWMBO and all that? Personally, I would just do a regrout, heavy scrub with bleach, and a good sealer. Cutting boards and plates would keep the food sanitary enough for me.
aem sends...
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yeah use a masonary or diamond blade to cut the grout if necessary
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