Bathroom floor 'tile'

Hi, next in the saga of the renters from hell <grin, actually I've heard of worse>.
The tub turned out to have a far worse leak than suspected.
Anyways, the tub is being replaced and we are a slab construction so the floor under is ok.
We have to re-tile the floor though later. These arent ceramic tiles, but the larger sort of acrylic squares. It looks alot like linoleum until you get up close and can see it's squares. Under them, are actual stone looking tiles that were not pulled up when this was applied over them. They are a hard to define greyish stone look. They might actually clean up nice but I bet some are damaged.
Can I lay new acrylic tiles over the older stone ones after removing the existing ones? It would be even easier if I can I just put new over the whole existing ones as they are very level and in good shape other than at the lip of the tub. I'm just unsure if 3 layers over a cement slab is 'ok'. On the other hand, it's possible these existing tiles are asbestos containing in which case covering them up is the safest easy way to go about it.
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You used that nasty A word.
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