Thanks for the reply - I'll add clarification:
Each of the 6 20A circuits has its own circuit breaker, 3 on one leg and 3 on the other. The box also has a proper tail, and has been seen, inspected, and signed off on by the fire inspector.
Working from memory, we used to have a breaker box that had two hots, a neutral, and a ground coming into it (does this imply 2 phases then?), with a fuse on each of the hots, and a rating of 220v, 60A. The only output off of this box was the 4 prong outlet (again with a proper tail). Recently, we had an electrician add in a box between the outlet and the breaker. The new box has one 30A 220v circuit, and 2 20A 110v circuits.
Based on how this seems to work, the new box has a limit of 6 20A 110v circuits, but the breakout box can only provide full capacity to three of those at any given time. So, we should pull three of the breakers out of the breakout box and limit that to 3 20A circuits, with two on one rail and one on the other. We should then add the 6th circuit into the new breaker box and mount a permanant 20A 110 outlet to the wall (for backline - the position is good for powering on-stage devices).
That leaves us with a 30A 220v outlet and a 20A 110v outlet for visiting companies which seems decent based on experience.
As an aside, this whole box is for audio power only, and is clean back to the main service entry to the building.