An unusual one ; what sort of asbestos floor tiles are they, do you have any info? What sort of floor is it, concrete slab, suspended or floating floor?
Tiling over tiles is never advisable & my advice is to take them up, any reason not to? At least then you know exactly where you are but if its bitumen adhesive under there, it will give you another problem although that may be the lesser of two evils requiring extra prep.
I’m assuming these are old type hard vinyl tiles For it to work at all they MUST be well fixed down, with no sign of any lifting anywhere but it’s OK to lift the odd tile & fill the void with addy. You will definitely need a quality trade, specialised adhesive, forget own brand or DIY stuff, it’s mostly crap anyway. You will need an elastomeric adhesive such as BAL Single Part Fastflex but it is expensive. The tiles must also be thoroughly clean with no trace of dirt, polish or other contamination or the addy wont bond well & if the tiles start lifting, you’ve just wasted a whole load of cash!
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