low pressure?

Where is your cold water storage tank/cistern at the moment? If it's a 3 storey house, it should still be in the attic/roof space. It would be unusual for it not to be at the highest point in the house - unless the 3rd storey was added later!
You would also need to know that there is sufficient mains pressure to take the cold supply coming into the house all the way to the where the cold water storage tank is going to be located. - E.g if a manometer (pressure gauge) placed on your service pipe from the main is only reading 10 m (1 bar), and your tank in the attic is going to be say 12 m above the point at which the pressure gauge was placed, the mains water will not reach the tank.
The hot water cylinder can be left on the 2nd floor - it will still be pressurized by the cold water tank and hot water will still be fed to the taps etc in a 3rd floor bathroom because the cold water tank is higher up. In fact it might be better to leave the hot water cylinder on the 2nd floor because this will minimize the length of dead legs - i.e. the length of hot water pipes which will contain cold/cooler water which has to be run off before you get hot water at the tap - in the house in general.
You can't or shouldn't do away with the cold water storage tank. It is there to provide you with 24 hours storage to supply sanitary fittings etc with water in the event of an interruption to mains supply (e.g. due to a burst water main). It also serves as an expansion tank for overflow/expansion from the hot water system. The tank is required by Water Bye Laws/Regulations etc.

JD
March 2009