Besides a fabricator, you most likely will need an electrician to move the boxes.

If you want it to match, it has to be from the same slab, and all be recut so that it miter matches. In other words, redo the island stone, after redesigning the cabinetry and electrical components too. You don’t just glom on a piece of stone to the side. That’s not how this works.

If your granite doesn't have specific movement and veining, search "butt joint waterfall counter" and you can see plenty of images. Is your overhang enough to cover the edge of another piece? I would talk to your fabricator first.

IMO waterfall counters only work in very contemporary spaces so maybe post a pic of your kitchen and BTW this needed to be done at one time the joints need to be mitered to look right too

I have a contemporary kitchen and the matching granite. I was asking if it is possible to add to the current counter at the edge to get the waterfall look.

If you’re willing to spend the extra 4-6K to redo the other things that need to be redone first, and you have the best kitchen designer, and the best stone fabricator in town, and that stone piece isn’t just from the same slab, but is the actual piece that was cut off from that end of the counter, and all the stars align, then sure. Otherwise, you’re doing all of the above plus buying a new slab of stone.

You need THIS result.

That can ONLY happen if the leftover piece is THIS piece. The one that is next to the piece that is your counter top . (And the money and stars align)

If it’s just a random off cut, like THIS, then you have to redo the whole thing.

Is it possible? Probably, but you wouldn't like the cost of my proposal, I'm sure.