Have you ever tried driving with only a pair or a single omni wheel deployed? Did it behave as I’m thinking it behaved? No reason (not for this year anyway) 
Most of the time Butterfly drives have a large reduction on the traction wheel from the omni wheel. We had a pneumatics problem a couple times and saw this but it didn’t look good since the omnis were trying to drive much faster than the traction wheel(s). Never attempted to do anything other than stop and fix it once we noticed it was happening.
We’ve had some butterfly drives where the omnis and traction wheels are 1:1, and we’ve tested it.
We call this 2+2. It works just like you’d expect. The turning point shifts in-between the two traction wheels.
We ended up with half an Octanum (Hexanum?) in 2011 due to weight. 4 mecanums, 2 lower geared traction wheels we could drop for extra pushing power, less turnability, etc. We just modified the drive mapping in the 2+2 mode to drive the mecanums less than the stickies. It worked fairly well for us. Yes, the pivot point moved between the traction wheels. Turned ridiculously well thanks to the angled force vectors on the mecanums.
Thanks all, that’s good feedback. I’m thinking of a way for a regular tank drive to shift its turning center relatively easily as a means to escape pins, “walk sideways”, or just drive better in forward or reverse. More to come this summer if I give some time to it.