I would like to increase my water pressure.

Yes, an upgraded pump would make a huge difference. Take a look at what's in your rig and you'll probably see a bottom of the line Surflo. Shurflo makes some good high-end pumps but they usually put the cheap-o one in most RVs.

Most RV pumps will increase volume but not pressure. You can do a little more pressure by adjusting the pressure switch.
I believe you may just want more volume. Standard pumps are around 2.8 GPM. Larger pumps go about 5.3 GPM (Aquatec) which doeas put out more pressure. Maybe more then some rigs can handle.

Replace the pump with Aqua Flow or one of the others with specs you like.
Ours came with an Aqua Flow, pump. It is 3.5 gal at 55 psi per literature with coach. It was replaced once, I think and not sure it is the same but it puts out more pressure than many or most campgrounds.
I like it at 60lbs or better at home. Afraid to do any mods to boost it in the coach as many express concern with the flexible piping used in them.
We've seen pressures of 80 lbs at a couple of campgrounds in Ky with no problems though.
We intend to use pressure regulator but one we have was belly up from the get go and to cheap to replace it.

If you increase PSI you need to increase all your tank sizes too. :B

There are water saver devices on the inside of the spout. Removing the one in our shower really helped with the pressure there. Just screw off the threaded end of the spout and there will be a round white plastic piece with small holes in it, remove this and see if it helps. All taps have them now. The shower piece is in between the supply hose and the handheld ....

If it's a Shurflo there are a variety of pressure switches available. They provide switches up to 150 psi. Your ability to change switches will depend upon model, motor and the cam your pump came with. The hard part is finding a dealer that has both knowledge and inventory