Pocket Wizard Mini TT1 question

PW Mini TT 1, Can this transmitter be used to fire a PW Plus II or the new Plus III, for that matter?

I have the Mini TT1 and a Flex TT5 for use with my Canon Speedlights but want to get a full size strobe like an AB for times when I need more power and distance. I dont want to have to buy another Flex TT5 at $200+ to be able to do this. I was thinking the soon to be release PW Plus III might do the trick at $139.

I know I could always remove my TT 5 from the 550EX and attach it to the strobe but was looking to have its own receiver to avoid the moving it back and forth.

Thx!