Prepping the surface of your tile, to be tiled, may be the same amount of money as it would be to remove to the subfloor, depending upon the texture of existing tile. Also keep in mind, when you tile over existing tile your counters will be shorter and all doors will need to be cut to accommodate new height of floors.

Technically yes...but any professional worth his/her salt will tell you not to do it. The one place it is possible = over cement slab. To remove the tiles = $1-$2/sf. To prepare the old tiles for new product = $1-2/sf PLUS cost of materials (concrete needs to be poured and allowed to set).

Here is what you need to know: to get a second layer on this floor = sanding down the surface of the old tile = $ + dusty. These tiles need to be ruffed up. Primer used over the ruffed up tile ($). Cement leveling compound to layer over top the old tile = $ + $ labour. Once the cement cures (could be a few days depending on how thick this is) the "real" work of installing the new tile. Now the "regular" labour costs + materials begins. Now the 2 projects are 'equal' in time and money.

Chances of having a successful "remove and replace" tile floor = 99-100%.
Chances of having a successful "two layers of tile" = 50% or less.

Which is faster: remove and replace. Which has greater chance of success: remove and replace. Which is "cheaper" = it is a tie...they will cost roughly the same. One has more labour the other has more materials.

Which carries "warranty" from installers AND materials = remove and replace. My decision is clear...but then again I don't own a tile floor.

for 145 years the various owners of my house put one kind of flooring over another in my kitchen until there was a 3" step up into the kitchen from all other doorways. it was a fir-linoleum-maple-linoleum-plywood-tile-tile sandwich. it was rock solid. but i wouldnt advise anyone to do that, it cost us a lot of time and money to get back down to the fir.

Thank you Cancork Floor...that is the most comprehensive answer I've received. I so appreciate you taking the time to reply!