As others post, running both elements at once wont noticably* increase the volume of hot water that can be obtained at one time, this is determined by the size in gallons of the tank.
Running both elements at once will however reduce the recovery time, and allow a greater useage in gallons per hour.
With a 3 phase supply, it should be possible to run 2 elements at once without overloading the wiring, provided that this was correctly sized in the first place.
With a 2 wire cable, the only option is to connect both elements in parralel, to the same phase, this will of course draw twice the amps, and overload a circuit intended for a single element.
If however a 3 wire cable is installed, to bring all 3 phases of a 208 volt supply to the water heater, then two elements can be utilised without any increase in current.
Connect one element between A+B and the other between B+C.
Although two elements are connected to the B phase, this conductor wont carry twice the current since the currents are out of phase.
Indeed, a third element could be connected between A+C , though that is of little use as most water heaters dont have provision for three elements.
Can the elements be replaced without replacing the tank ? UK ones can. If so it might be possible to install higher wattage elements, so as to fully utilise the ampacity of the existing circuit.
Another option might be to raise the themostat setting as high as possible, and fit a tempering valve to the outlet to avoid scalding.
This will in effect increase the storeage volume since say 25 gallons of near boiling water, if diluted with cold, might produce 50 gallons of water at utilisation temperature.
*To be pedantic, running both elements at once will VERY SLIGHTLY increase the amount of hot water that can be used at once.
To draw of the entire tank contents will take several minutes, and during this time more water is being heated, therefore a 25 gallon tank might provide 26 gallons of hot water, another gallon having been heated whilst the water was being used.
Doubling the loading will double the amount of water being heated whilst the water is being used, perhaps from one gallon to two gallons, therefore increasing the total amount from 26 gallons to 27.
The difference is unlikely to matter in practice.
Here in the UK I once fitted heating elements of 18KW in total to a relatively small hot water tank, this heated the water as fast as it could be used from a single outlet, and kept up with heavy use of 4 or 5 showers.
With a 3 phase 240/415 volt supply, the line current was only about 25 amps.