That's what active basses are for. To me, that looks like unnecessary fiddling and a nightmare on stage (I play a passive P bass and am constantly worried that my volume knob is not at 100%) as there are simpler ways to alter your tone (moving your plucking hand, EQ pedals, preamps, etc.), but if you really must have the ability to blend the 3 pickups with various volume knob combinations, 3 volume knobs are necessary, so you need active circuitry to keep a healthy signal.
If you could swing just two pickups, a blend knob would be the most efficient way to favor one pickup on the fly, and it would be easy to use on stage too.