Guidelines for re-plumbing a house (bathroom in particular)?

The main thing to prevent burning oneself in a shower is to install a pressure balanced or anti-scald shower valve.

This type of valve is supposed to keep the water temp from fluctuating more than a few degrees up or down.

All of the major brands offer this feature in their single handle faucets.

Moen positemp.

Delta monitor

Others have equivalents.

Who is using the toilet while you shower ????

When the toilet is flushed, there is a large volume of water flow, which reduces overall water pressure.

Check the water pressure in the line, and many houses have a pressure regulator near the main shutoff. It can be adjusted.

Often the supply line is reduced from 3/4 " to 1/2" right after the shutoff. It is quite easy to install a 1/2" take off right on the 3/4" line, then run it for the bathroom cold water circuit.

Often, the whole house is plumbed back to the hot water tank on 1/2" line. You could increase the feed line to 3/4" and and use a manifold for 1/2" takeoffs. This would also be a good time to increase the cold water line to the hot water tank to 3/4", or use a dedicated 1/2" line from the 3/4" main shutoff.

You can also restrict the water flow to the toilet. Even though the toilet will fill slower, it will reduce 'shower shock'.

Install a low-flow energy efficient shower head, and a temperature sensitive/adjustable tub/shower faucet.

The whole premise is to reduce pressure and flow restrictions to each appliance, thereby increasing the final pressure and flow rates at each appliance.

You start by checking the incoming pressure and sizing the piping - main & branches. You look at demand in the entire house (not just the one bathroom). If the incoming pressure is much under 40 psi, you see if there's something you can do about it.

Causes of poor water delivery can range from under-sized piping to old galvanized piping (which has scaled to the point where it's under-sized) to a valve that isn't fully opened.

I don't know for sure if this will solve your problem or not.

I've seen homes that have a manifold at the hot water tank with seperate lines running to each plumbing fixture from the manifold. It is supposed to equalize the water pressure.

in the US plumbing needs to be done by a licensed plumber and inspected. if you are not in the US then you need to check your local building codes...

nothing just time your showering with using the toilet