I have about a 200 SF kitchen area with two layers of tile. The bottom
layer is very old, probably installed 40 years ago or more. On top is
a layer of stick-on Armstrong vinyl I installed myself about 15 years
back. For various reasons (because SWMBO wants to being in the
forefront), I'm facing the prospect of putting down a new floor. The
area is sufficiently irregular to make one-piece flooring impractical,
or at least uneconomical, so we're looking at other stuff, such as
the engineered wood products or ceramic tile.

Most of the existing floor is tight & in decent shape, save about 10 SF
in front of the dishwasher (thanks to a chronic but undetected leak)
and another area where a cabinet was removed.

My question is the eternal one: Do I take off the two layers of
existing tile first, or can I go directly on top? I understand that
for the tile option, I would be adding ¼" of cement board and
another ¼" of tile on top of an already raised floor. I can live
with that.

Whether or not I need to is another question, and raises more
questions. Is the old tile likely to be a royal pain in the ass to
remove? Were there asbestos or other potentially hazardous materials
in the old tile that would be better to leave in place?

Alternatively, all of the loose and damaged tile is only the top layer.
Is it likely this will be more easily removed? If so, I'd be
comfortable with a direct application of a thin material on top of the
old.

Lastly, do you have any recommendations as to other flooring products
for application above two layers of tile?

TIA,
Joe F.