In my band, I'm fortunate enough to be able to afford Fractal gear, but unfortuantely the other guitar player is not in a position to buy higher end gear. His gear doesn't sound as good as I would like, so I used my Axe FX II XL+ for both guitarists, controlled with my MFC-101. I used 5 scenes: Both Clean, One Clean/One Dirty, the Other Clean/Other Dirty, Both Dirty, and Dirty Rhythm/Solo Boost.
Since I am the lead guitarist and lead vocalist, it got to be quite annoying controlling both guitars while playing and singing, but it was doable. I eventually got an AX8, which the other guitarist now uses. This is a much simpler/better solution for me. If the scene selection was automated or if there was less busy (or more capable than I) person, it would totally work.
I think with the Axe FX III, if they made one or two changes, it would be doable, especially with the FC6/FC12 paradigm.
1. Four amps at the same time with 2 channels (rather than 2 amps w/ 4 channels), would work better for this
2. A virtual A/B/Y FX Block, allowing a MIDI command to switch between FX chains.
In this way, any player could switch between a clean and dirty amp, with all associated FX, independently of the other Player's FX chains and the FC series would be simple to implement for this kind of use.