I've had a couple of customers recently asking for new double sockets to be installed on an existing tiled wall in a kitchen. The walls are hollow so relatively easy to feed the cables through but I can see cutting the tiles in situ being a challenge without damaging them. Only think I can think is angle grinder but ain't gonna be easy. Anyone else get asked to do this much? Walk away??!
Just done same in my kitchen, fitting extra sockets, used my Bosch multitool with a diamond blade,to cut through the tiles, no damage, can access right in to the corners without over cutting,& have a nice neat hole for the box, it wasn't easy to do though, as vibration loosened one tile, as tile adhesive was only spotted.(not my work) But,I expect the blade might struggle on really hard tiles . Walk away is my advice.
Small angle grinder with diamond tipped blade or as Kiab suggested a multitool. I have a Fein Multimaster which does the same job but they are too expensive to consider for a one-off job.
Don't have a diamond blade for my multitool but Screwfix do a cheapy Erbauer diamond blade for £12.99 - will hopefully last for one job and the customer can pay for it. They're just ceramic tiles so shouldn't be too bad to cut - famous last words! Of course it's a new build and the customer could have just paid the builders to fit sockets before the tiles went up for £60, but they thought that was too much. Min £100 for this job. Cheers guys!
I had to cut some floor tiles back by around 25mm after the builder had layed the tiles too far into the door threshold, so you could see them in the next room when the door was closed (this was for the mother in law) I drilled a series of 5mm holes with a tile drill, then used a diamond blade and multi tool (being a diyer just a good old green Bosch) I found the blade can skid a bit on the tile surface without drilling holes, but with the holes, the blade can bite into the tile and cut relatively easily Obviously you don't need a perfect cut edge as the socket will allow a slight overlap
I also found that you have more control using a multitool than with a small grinder cutting the tile.
I would advise telling the customer, if you do decide to take this on, that you cannot guarantee no breakage of tiles. Secondly, cutting carefully through a fragile wall finish takes time and care so in theory should attract a higher price. If the customer is wanting a difficult job doing then they need to be aware of the potential consequence of breaking a tile and the fact it is much trickier to do. I don't suppose they appreciate that.
If the original back boxes are fitted before the tiles, these will take time to cut out. Possibly your new back boxes will not fit in the same hole, (back box edge over tile), so you will have to grind back the tiles behind the original socket. Tile drill holes in all the corners first. Make sure there are no studs behind your new hole. Plastic dust sheet everything in the kitchen. Ensure the back box clamps have enough depth for plasterboard and tile. Tape over bare (now dead) cables before pulling through old boxes. Is there enough cable to fit to the new socket. Would you think I've done this before. Can be very frustrating, but rewarding. Charge loads.
I have done this a few times, and have used a small tile drill to stitch drill around the socket. I took the kitchen kick plate off and used a bradawl to find the vertical stud from below, to make sure the socket would hit one, and sink a back box into it once tile and plasterboard clear. I would try to avoid cutting between the studs, as a dry lining box is not great on sockets. If the tiles were expensive, I would advise customer against, as they will likely be extreamely hard (which is good in a way I guess, as less likely to break), but will also be expensive to replace, lol.