re-reading from the original post
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One brother frequently has nieces and nephews staying over and wanting to use water at same time.
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This is a VOLUME problem, not a pressure problem.
It is possible that the entire house is plumbed with 1/2" copper,like mine, so opening 2 or more taps reduces water flow to all of the taps and closest to the pump 'wins the water'. Increasing the pressure can push the water further,but won't increase the GPM, except that the water gets upstairs faster.
Other tidbit is that the pump is rated for xx GPM. That's really the starting point. If it's rated for 6 GPM, no way you'll get 10 GPM out of it.
To get more water(GPM) you need to increase the pipe diameter. double the diameter, x4..triple = x9.
Wife wanted to water her veggies. She laid out 1200' of weeping hose all in series(end to end to end to ...) connects to well pump fed from 2000g tank. hmm, didn't work. I made a header from 1.5" ABS, 9 takeoffs, each 100-130' long. Works like a charm ,ALL the veggies were happy.
Every new house today is 'PEX plumbed' and has manifolds to allow the 3/8" PEX to 'work better than copper'.
Most (all ?) faucets and shower heads today have restricters in them , like 2.5GPM.Those allow better distribution of the water