Retiling a bathroom vanity

Looking for opinions ...
The current vanity top is 4" white tiles, backsplash of same, bullnose at front. Looking at the sink cutout from underneath, it seems like the tiles are set in a mortar bed (wire mesh, and about an inch of mortar, over ply).
Googling, it seems that removing a mortar bed is a PITA, and tiling over tile is an option. Further, since I tiled the floor, the counter is a little low - so the added height would be a plus.
I'm thinking to remove the bullnose (so I don't end up adding depth) and backsplash, and tile upwards from there.
Does this sound reasonable? Should I thinset in a layer of hardi, then tile, or just tile? Sand down the tiles first, or just latex-modified thinset?
TIA, JSH
Bonus question: the current sink is a drop-in, but I'd like to use an above-counter / vessel style sink, so I'd need to fill in some of the cutout to support the tile underneath the vessel. Ideas?
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if they're stuck down well, then you can tile over it, although i think it'll look odd and really thick. you could just bust them all off, sand it down level (it doesn't have to be perfectly flat, just use more thinset than usual), and start over if you didn't want to take out the mortar bed.

that'll make tile on tile harder. it'll be hard to make a partial hole filler be strong enough to support the sink (and someone who accidentally leans on it). you'd have to have a ply backer, followed by enough mortar to raise it up to the top of the existing tile.
if you are going to do this, rip off the entire top and start over. build it up with 3/4 plywood and put a layer of hardibacker on top to tile on if you don't want to do another mortar bed.
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