All will of course depend on supply but 9.6KW = 42 amp so 4 x 9.8 = 170.4 Amp and normally the home is supplied with 100 amp max as that is normally the rating of the consumer unit so it would not take long before the fuse would blow but you can overload for a limited time so you may get away with it for some time. A 100 amp three phase supply would not have a problem with this load so not a simple answer "No" there are ways it can be done. but a storage device would make more sense. Even if still heated with electric it would allow multiple showers without tripping well worse really blowing the incoming fuses which would take some time to get renewed.
Storage is your answer. Mains pressure storage tanks are now availably you can use very small heater for long time to give hot water for short time. Not cheap Â£500 for tank Â£80 each for shower controls plus heater will work a lot better than any direct electric heating. There are other ways by making it impossible to use more than one shower at a time. Four contactors and four current switches can basically turn off other three showers once one has been switched on. Even if you use gas or oil to heat the water to use four showers together you need storage.
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