[Thalas_shaya]

So my feeling is that you will need the pump to be always on, because you will have some tanks getting continuous flow. If pressure stability is the chief concern, then you could accomplish this with a variable speed pump, running it at a higher rate when 80% of the tanks are receiving water and at a lower rate when 30% are receiving water. If power efficiency is a greater concern than pressure, you can use a pump that is minimally sized to accomplish your goal of filling tanks simultaneously, and simply allow the pressure (and thus, flow rate) to drop off at high demand times.
Happy to discuss further if his sparks questions or if my answer is unclear.