Removing tiles over tiles!

I refitted my bathroom about ten years ago and am about to do it all again. When I did it previously, I tiled over the top of the original wall tiles.
I am hoping that when I start to remove the old tiles, they will come off the original tiles fairly easily (because they are stuck onto a glazed surface). Is this likely to be the case - or am I going to end up having to remove both 'layers' of tiles?
I have removed wall tiles before - but never attempted to remove a top layer of tiles off an under-lying layer of tiles.

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