It's relatively easy to do.
Just use a two pump / blower system will allow you to control 3 pumps, however, you can also switch multiple sets of relays with one push-button.
About 7 years ago I had a special application that needed 3 pumps and a blower, so I just added an offboard double pole relay to one of the pump outputs. So, when the user turns on that pump, it kicks in the offboard relay which turns on two pumps instead of one.
IRT your question, yes it is probably a proprietary controller. They use what are called vfc zones, where each zone will control (turn on and off) it's own pump, so, they aren't really switched thru the main control system.
That said, their brochure indicates 3 MBHP. So you can take that to mean 'locked rotor' current measurement, which in reality means more like 8 amp maximum pump motors - eg 1.5 hp at 230 volts. Typically, an 8 amp max pump motor will run at less than this, (the impeller size controls the actual current draw from the motor), so we'll estimate 7 amps for the sake of simplicity.
5 X 7 amps=35 amps for all the pumps.
Add in 1 Amp for the Vico circ pump.
That's 36 amps for everything, then they're touting the intelligent heater, which in most respects, is probably a heater element with multiple wattage taps. Those taps will typically be switched in accordance with the number of pumps being turned on. (More pumps on=lower heater wattage).
But for a 69 jet tub, one doesn't really need 5 pumps, especially where 30 of them are micro-cyclone jets. I just finished a 52 jet tub using 2 4hp pumps that totally kicks butt.
Last thing, what really suprises me is that all I can see are 4 main suctions at the bottom of the tub, and the filter cavity, which means that all 5 pumps plus the circ pump are sharing these suction lines.
Which should give you a clue as to the actual gpm necessary to power all these jets/pumps... not as much as it actually seems - and that's where a tub's power actually is, the number of jets, and the actual total GPM of the pumps and pressure output from the jets on the medium pressure output rating scale.
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