Yes, you can do this. I can't think of any reasons why _I'd_ ever want to do this, but it can be done. You'll need to scarify the surface of the old tiles with a grinder so that the surface is rough enough to allow the new thinset to grip tightly. This will be messy. You'll need to get mudring extensions for your existing electrical boxes to accommodate the additional tile thickness. Take a close look at any areas where your current backsplash meets up with trim around your windows and doors - the additional depth may affect the look in those areas. Look at where your BS meets the cabinets & hood or OTR microwave to make sure the added thickness won't cause unwanted issues. And finally, make sure it won't encroach too much on any sinks or faucets. Backsplash tiles usually come off fairly easily and repairing the underlying substrate is usually a quick and easy job. That's the route I'd recommend unless there's a strong contraindication against removal.

Thanks dseng! I'm sure I will do it the right way and remove the existing bs. How do I remove the current tiles? Sorry for all the questions, but this is the first diy project I have ever done! I'm determined to do it myself and for it to be done right and look good!

This is actually a great DIY project to get started with. Tile removal on a backsplash is a simple task, but can require varying degrees of elbow grease. Tools - a hammer, cold chisel (masonry chisel), a thin bladed prybar, a stiff bladed putty knife, eye protection, and gloves can usually get the whole thing done. A shop vac is handy to clean up the inevitable mess - don't use your regular vac unless you're itching to replace it. If there's an exposed edge, that can be a good place to start, otherwise you'll need to break a tile (use the hammer and cold chisel) and chip out the pieces to gain a spot where you can start to work your prybar or putty knife behind the tiles and pry/pop them off. You'll most likely need to drive this behind the tile(s) with the hammer. Sometimes they come off easy, sometimes they'll take the underlying drywall with them. The basic idea is to work in behind the tiles to get each one off whole, rather than trying to break them up from the face side. Once the tiles are all removed you'll need to repair or replace the underlying drywall depending on how much damage was done during the removal. Once you have a new, smooth, fair surface, you can get busy putting up your beautiful new backsplash.