Back in 2009 I printed out the pitching staff rosters for all 30 MLB clubs and then went to gettyimages.com to view as many stills taken at or near release point as I could find for each of the ~400 active pitchers.
First, I was interested to know about how many sidearmers were pitching at that level and, second, I became interested to know how many pitchers showed clear evidence of pitching with more than one arm-slot.
The study had flaws, of course: There were photos at or near release point for only about 340 of the 415 - 420 active pitchers at the time, and in some cases there were only one or two usable photos of a given pitcher.
Nevertheless, at the time it looked as though about 10% of MLB pitchers were sidearmers, and perhaps 2% of MLB pitchers gave clear evidence of using two different arm-slots. There could be more than 2%, but I doubt if it is greatly different than that. I didn't see any evidence for pitchers with three distinct arm-slots.
Bum is right, the two-armslot guys almost always threw sidearm from one of them. Some, like Mike Meyers went submarine with their 2nd arm-slot. Others, like Bronson Arroyo went 3/4 with the "other" arm-slot.
It looked like Randy Johnson went side-arm when he threw the slider, low 3/4 when he threw the FB.
Ultimately, I personally agree with Bum...if a pitcher can command several pitches from one armslot/release point he is doing very well and should continue to refine that. Simple trigonometry shows how shockingly difficult it is for a pitcher to control the strike zone from just one "repeatable" release point.
I would never try to talk a young pitcher out of experimenting with his delivery, but on the other hand I wouldn't try to talk anyone into adopting "multiple arm-slots" either. It doesn't look like very many pitchers can control two different arm-slots, much less three.