Can I lay new tile over old thinset?

Construction (stucco siding and tile roofs, I have several 20 year old roofs that should go another 20 years in their sleep, I paid $7500 to reroof a 12 year old property on MN) and age property.

So I had another contractor do a walk through of the house to give me a new quote and he informed me during the walk through that there were chances asbestos existed under the floor tiles and that the previous contractor may disturbed it when he had them removed.

Cabinets, floors tiled walls and floors etc.Then with modern technology we video walk through the apt. 

I am finding even though you dont really hit the rules that are on BP. 1%  2% was 10 years ago.no income tax. and property Taxs half or more of other markets so cash flow is not as bad as some would think when you add that all in. plus late model houses which are all built with stucco siding and tile roofs and NO hail  and desert landscaping and soil that does not move..

That being said my $11,000 reno budget is mainly for repairs that are cosmetic like flooring; paint; tile and baseboards etc. 

Main bathroom has all new fixtures and custom tile.

Main bathroom has all new fixtures and custom tile.

Some window and door screens need to be replaced9) Substantial damage to the tile on the back patio10) Detected mold-like substance in laundry room and bathrooms.

Now it an 450 sq ft SFH on a slab with ceramic tile floor .