Would increasing pipe size just after the meter give better flow without increasing pressure too much?

The inside diameter of half-inch copper pipe is 0.527 inches. The inside diameter of three-quarter inch Pex is 0.681. That means that the Pex you want to install can theoretically carry about 29 percent more water than copper.

Keep in mind that PEX-a has the same OD as copper and has a thicker wall resulting in greater insulation and will not sweat like copper. PEX-a is 3 times smoother than new copper which means water is moved at greater velocities, this helps to reduce the difference in flow characteristics when comparing to equivalent sized copper pipe and the slightly smaller ID of PEX.

That said, there are other factors to consider that can be hard to calculate precisely. One is how many fittings you have; since Pex fittings go inside the pipe instead of around it like copper, each fitting that you add when using Pex reduces the flow rate. Right angles also decrease the flow rate since water has to work harder to go around hard turns -- although here Pex can be advantageous in some cases because you can curve it around corners, whereas with copper you'd have to use an elbow.

Also, if using PEX-a, like Uponor AquaPex, the cold expansion fittings are almost the same ID as the PEX line itself and provides a 29% larger ID than regular crimp fittings like ASTM F1807/F2159. This results in a 70% greater flow over standard crimp fittings. For example, Uponor Propex 3/4" fitting has an ID of 0.595" compared to the 0.681" ID of the PEX line itself. The plastic 3/4" crimp style fitting has an ID of 0.460" and the brass crimp style 3/4" has an ID of 0.530".

The number of fixtures being served by your lines of Pex could also make a big difference. Ideally, you'd have a dedicated run of Pex (i.e., a "home run") going directly from the water meter to each bathroom. That would likely result in a much better experience than tying both bathrooms into the same line. Of course, running a dedicated line to each bathroom may or may not be feasible, depending on where the bathrooms are located and how many walls you'd have to cut up to do this.

The location of the bathrooms matters, too. If one is on the third floor and the other is in the basement, the latter might rob the former of water when it is in use.

The bottom line: Without a lot more data about the specifics of your situation, it's impossible to say for sure whether replumbing with Pex would increase volume. But it probably would, especially if you are careful to avoid unnecessary fittings within your Pex lines and you are able to do a dedicated line to each bathroom.

All this said, half-inch copper (and, for that matter, half-inch Pex) should be sufficient to serve two showers in most cases. I have a three-story house with three full baths that is plumbed with a mix of half-inch copper and half-inch Pex, and never have issues with the showers. But I also have a 1.5-inch line coming in from the street, which could be a factor. I wonder if your real issue is that the volume of water coming off the street is just too low; do your neighbors who have multiple bathrooms have any issues?

Bad idea. Enlarging hot water lines will dramatically increase the inventory of water sitting in those lines. I.e. How much water is in the lines themselves.

I.e. How much cold water those hot water lines are full of, when you first turn on the shower.

I.e. How long you must wait for the cold water to be pushed through and become hot.

You reduce droops by not allowing any one appliance to suck up all the water, and you do that with flow restrictions. The single best thing you can do to ease water droop is fit low-flow showerheads. Of course, if it's a shower only, with no tub diverter, that means waiting even longer for initial hot water.

Here's how I'd fix that. So I would couple that with minimizing the size of the water pipes, and have a homerun for each shower, for both hot and cold lines. And tap both right at the top of the water heater. That will ease pressure droops, and pressure droops will affect both hot and cold equally, so no chilly/scalding surges.

So for instance a 3/8" run just for each shower. A 3/8" pipe has 1/4 the inventory of a 3/4" pipe, so it warms up 4 times faster. Such a small pipe would make sense given your high water pressure and a low-flow head.

Here is something I did in a friends home. I/we changed the 1/2" copper water line to 3/4" copper from the water meter to the hot water tank and teed off any existing cold water supply lines. That way, both the hot and cold water lines would utilize more water while not spending a lot of money to replace all or even some of the individual 1/2" supply lines. It worked great and his wife and kids were happy. Now, if you want a good shower nozzle that is not expensive, try a Delta model 52650-PK which can be bought almost anywhere that shower products are sold. And, I might add that the girls will be happy. Mine was special ordered through Home Depot for less than $20.00. I have been using this style for 40 years. (check it out) As for the water pressure, There should be no problem with the pressure at 85# or even 100#. Mine varies from 70 to 95 psi during the day with no adverse effects and no PRV to screw with. The only water filter I use in my house is a whole house filter, mounted under the kitchen sink that has a charcoal filter to take out the bad taste of the city water, which is where we get all our "drinking" water. I replace the charcoal filter every 6 months. (my 2 cents)

I didn't read all the answers and comments but,

The pressure of the static system will not change due to the pipe size. A quarter inch line will experience the same pressure as a 1-inch line with all valves off at the fixtures. The difference between a quarter inch line and a 1-inch line is when there is flow, or dynamic pressure, you will get more pressure drop on a smaller line. Any devices or fixtures attached to your plumbing system that have a maximum pressure rating should have a pressure-reducing valve installed just for them as installing a pressure-reducing valve on your whole system will greatly reduce your flow. Three-quarter inch PEX is in practice of roughly the same size as half inch copper especially if you're using many fittings as they are smaller then the 3/4 PEX itself. As a matter of fact the Pex fittings have a smaller inside diameter than copper pipe but you do it being such a short piece it doesn't have an overall smaller than copper pipes effect. Home run systems work great it will however exclude any possibility of hot water recirculation. One thing nobody does with a home run system is Supply the Home Run manifold from both sides that way you always have equal flow I don't know why this isn't a requirement from the manufacturer.

This is a proper home run system Poorly drawn in my truck while eating lunch.