It happens all the time. Usually a consortium of banks who trade a lot with each other decide it's going to be easier to set up a separate organization to handle all their interactions. I worked on one a few years ago, Centradia, which was a private exchange that 5 banks used to pool liquidity for foreign exchange dealing. Thera are quite a few, and no-one outside the industry will ever have heard of them. A mate of mine's at Equiduct now.