"There is a thingie that can be added to the pipe coming out of the tank, that will mix extra hot water with cold water so that the result is just plain old hot water but a whole lot of it. After installing it, you raise the temperature in the tank to a very high temperature and then the mixing thing brings the two "waters" together (extremely hot, and basic cold) and you get a whole lot of plain old hot water. Like double."
It's called a tempering valve. It allows you to set the water heater temperature to about 160 or 170 and mix it with cold using a temperature controlling valve so that you get more water in the desirable range.
It allows you to store more heat in the tank, but it doesn't help the recovery on an electric heater.
It requires both a cold and hot water inlet, and a not-so-hot water outlet. Your plumbers will know what it is and may have one on the truck.