Running a gravity cold feed to the existing shower mixer would usually be a better solution to the problem.
Differing water pressures for the hot and cold supplies often ends up causing a hatful of headaches, from over-sensitive temperature adjustment or wildly fluctuating water temperatures through to water backfeeding up the hot supply, no matter how many bells and whistles the shower mixer has.
Some use pressure reducing valves or pressure equalising valves in the cold supply, but a gravity supply is less complicated - and gravity is free (at least it will be until the government work out how they can tax it!)
Differing water pressures for the hot and cold supplies often ends up causing a hatful of headaches, from over-sensitive temperature adjustment or wildly fluctuating water temperatures through to water backfeeding up the hot supply, no matter how many bells and whistles the shower mixer has.
Some use pressure reducing valves or pressure equalising valves in the cold supply, but a gravity supply is less complicated - and gravity is free (at least it will be until the government work out how they can tax it!)