You can mod one to work like that, but that's about it.
Most ambi-mice have buttons placed for a lefty thumb, which I find has the disadvantage of being caught by the third finger all the time. It's a right PITA and the one major con of my Roccat Kova.
There are mice with third finger buttons, which would make them pinky buttons if you usually 'three-finger' your mouse, ie you have your middle finger on the scroll and use your third finger for RMB.
If that's the sort of thing you meant, Logitech's G600 has one and I believe Coolermaster did a few mice like this... They also have the Storm Inferno, which has buttons outside of both RMB and LMB, which you might find useful.