Not very successfully. I'd remove the granite and do it correctly.

I agree that the BEST way would be to remove the granite, but that could be a huge project. The biggest concern with going over the existing backsplash is getting the new tile to bond well. One of granites best features is the ease of cleaning the surface so getting something to stick to it may be difficult. You could experiment with a small area and a couple of new tile. The granite would need to be sanded with very coarse sandpaper to reduce the glaze. Go to a local tile supplier(where the pros go, not a big box!) and tell them what you're trying to accomplish. They will give you a tile adhesive that will PROBABLY work(no guarantee!) Let the new tile stick for a couple of days and try to pry one off. If it's fairly difficult, then this method might be ok. If it comes off easily you're in for a major demo project! Good Luck!

Some short cuts can make for long frustrating issues down the road. My gut tells me to do it right, pull out what you don't like and put in what you want.

i'm assuming you are talking full height granite backsplash, not 4" tall job.

i'm for trying to put it on the granite. whether it has a layer of tile glommed on top or no, the granite won't come out easily down the road. in for a penny, in for a pound, its going to need the wallboard behind it replaced either way.

BUT before you stick tiles on the 'easy parts' you have to work out what you will do on the hard parts. having an end view of granite backsplash with tile stuck in front isnt acceptable. if the backsplash ALL ends at cabinets or walls you are lucky.