Probably, but you probably won't like the results. The edge pieces, corners,
etc, are all designed for 90 degree corners and may not fit well. Odds are
if you put a straightedge along counter, it also isn't perfectly flat, which
is hard to tile over. And you don't really save much labor, because sink has
to come out anyway, along with any electrical outlet in tile field. You can
try it as DIY, but if you were going to hire it out, a good tile guy will
refuse, due to more likely callbacks and bad word-of-mouth from a job that
looks funny. Demo work for a counter would only be a couple hours at most-
maybe a little longer if they used mastic over wood, and you need to overlay
with backer board or something. Odds are once you get a corner started most
will pop right off. (in my experience, at least.)
I keep reading that you should tile over the old tile rather than pulling
them off. I'm guessing edging tiles or bead along the edge to finish off.
When I retiled a kitchen leaving the old ones on would no doubt have made it
easier to get them even. Though I'm not sure what happens when you have 2
layers of tiles and fancy a change...
Of course the other option, which I would probably choose now, is to use
tile paint on the old tiles. You can also get tile primer which allows you
to use "normal" paint on tiles too - probably the best option to get a
better match/choice of colours.
Although, re-reading your post, it sounds like these tiles actually make up
the working surface of your countertops, which I don't have experience of
and I'm not sure if tile paint is suitable for that. But I'll send this post
anyway, might help someone intending to work on splashback-type tiles.
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