We cannot even open another cold water outlet in the house, so treat
manufacturers claims with care. The reality probably depends more on your
setup.

If turning on a cold tap elsewhere in the house affects the shower, then the
problem is entirely with your cold water mains supply, or too thin pipework
within your house (or even a half closed stopcock). The boiler does not
appear to be at fault.

You may find things better if you install a pressure balancing valve just
before the shower. This will at least stop blasts of cold or hot water when
a tap is opened. You can also turn down isolating valves on the downstairs
taps to stop them hogging all the flow. However, the basic problem is that
the street is not providing as much water as you wish to use.

If the worst comes to the worst, you can feed the combi boiler off a cold
tank in the loft. At least you've still saved the cylinder space.

Christian.