I have a 3000 gallon water storage tank that my 4 inch well pump (800 feet down) fills up and the water tank then gravity feeds about 5 feet into a shallow well pump that pumps water into a 60 gallon pressure pump about one foot away. The pressure pump sends water to the house about 300 feet through one-inch pvc pipe into the house. The shallow well pump and pressure tank are located inside my pump house. The water pressure inside the house is OK but I would like it to be much higher than it is. Can I cut into my one-inch water line right before it goes into the house and install a second pressure tank and then connect the out pipe to the water line going into the house and if so, will it raise the water pressure substantially so that the showers have more pressure and etc. or would I have to install another shallow well pump before the second pressure tank or am I wasting time and money on all of the above. I can live with it the way it is but it would be nice to have greater water pressure coming out of my spigots and shower heads. Thanks for any advice.
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
Because the output of your 3000 gallon tank is gravity fed. Get a Grundfos MQ pressure boosting pump. No external pressure tank, switch etc needed. It's built to turn on as soon as you open your faucet. We are using one in a similar situation and are very happy with it.