No mark I am not talking about a bladder type tank, I am talking about a open topped tank with an overflow. probably 500gal capacity or a couple of days capacity, you would have to check if this system is a Registered Air Gap for Backflow purposes in your area?
The incoming water would go through a Ball Float valve to fill the tank, you would connect a pump to the outlet to give the required pressure. I suggested a constant pressure type pump to avoid the high & low pressure of a pressure switch type pump. This is very annoying while under the shower.