Yep there is. Its called a cutback or a flat saddle. Here is mine, its not the top of the line, but it is a nice older barnsby. They are designed to set the rider a little farther back to allow the freedom of movement for the shoulder.
I was cleaning it, please forgive the sock under the flap. My Barnsby.jpg
Ill find a pic of a ss Friesian, give me a minute.