This depends on what your current plumbing system looks like.
If you have 3/4 inch copper coming into your house and 3/4" copper into the shower valve then yes you would have to upgrade your whole house - doubt this is it.
If you have 3/4-1 inch copper coming into your house and 1/2" copper on the shower valve line then you would just have to upgrade that line. That might be easy or very very costly because sometimes you have to open up walls that you don't want to.
Whatever it is you need to figure out where the shower valve branch diverts from the main line. Then you can see if the branch is smaller or if it is easy or hard to get to.
That sounds like an overly complicated setup with far more pumps than it should need. Or else you said pump when you meant tank in two places, actually, re-reading it.
In short, you can have as many pressure tanks as you like. Locating them closer to the point of use (the house) would be helpful, to a limited extent. That limited extent is the "effective volume" of the pressure tank at the house - while it's got pressure, you get better pressure at the house. As soon as it runs out of water and you become dependent on the pump, the pressure loss of the 300 feet of 1" PVC to the house comes into play, until you slow down your water use to the point where the pressure tank at the house fills up again.
If you do not change the setpoint pressure, the peak water pressure in the house will not be affected at all. Once the pressure tank at the house is depleted, the pressure will be the same as it is now. If you have a pressure gauge at the house now (or can add one) it might be useful to know the pressure at the house when "loads of interest" (showers, say) are drawing water.
Most pump controls can be altered to have a higher setpoint pressure, and most well pumps will provide that, within reason. General recommendations are to stay below 80 PSI - but if you are now running your pump on at 20 off at 40 (a typical default) you could turn it up to on at 30 off at 50, or on at 40 off at 60 - you will need to adjust your pressure tank (and any you may choose to add) for the higher pressure, particularly if they are bladder-type tanks - with the system drained, a bladder tank should typically be 2 PSI less than the low water pressure setpoint (ie, 18, 28, or 38 for the three ranges I've just given) and you may need additional pressure tank volume (because the effective volume of water a pressure tank can hold goes down as the system pressure goes up.) So, you can probably get more pressure without another pump, and possibly without another tank, but we'd need more details of what your system is doing now to know that for certain.
Unless your water use is extreme, 300 feet of 1" PVC pipe should not have a lot of effect on the pressure - at 5 gallons per minute, about 2.2 PSI - at 10GPM, 8.2PSI, 15 GPM, 17.4 psi
Best Answer
I don't know if there is an absolute minimum for your area. A pressure gauge can be installed on a kitchen faucet with a adapter to quickly check the pressure.
A few years back a family needed 120 psi for their child's medical needs. I installed a check valve on the main line and then a small booster pump and pressure tank. It was a small pump; I think it was 7gallons per minute. This provided both the pressure and flow they needed. The total cost was close to 1k for the pump tank and install. I also set it up so they could take it with them when they moved.
We had to replace several older valves that leaked due to the high pressure. Their original pressure from the city supply was just under 60. You need to be aware of the possibility of leaks with a pressure increase but you probably won't need such a high pressure.
Also we measured the flow afterwards and had much more than the pump was rated for, probably because the supply pressure to the pump was rated for a shallow well so you may not need as high a flow pump as your total demand.