We have 3 showers in the house. What can I do to have 3 people taking a showers at the same time a not run out of hot water?

You have few options. Raise the heater temp but that can be dangerous if you raise it over 120 degrees. Option 2 is buy a larger heater and lastly you can install a tankless heater. The one I have can run 3 showers while the washing machine is running. Me being cheap, I would just make my kids wait until I was out of the shower.

If everyone wants to shower at 1 time, a MUCH bigger HW heater is needed, particularly if ladies involved with hair etc. What gallon do you have now, Gas or electric? You can put a timer on the showers, or do 1 shower at a time with a time limit.