Does amp output V decrease by adding gain stage?

You can add as much gain as you want before or at the input of the amp but it will not change the amps output in any way. IOW whatever it is rated at in terms of full output wattage will be the same. What you will change is the sensitivity of the amp. IOW you won't need 4 volts to get the amp to full output.

Is that the input sensitivity? Balanced or RCA? You might need one hulk of a preamp.

That is RCA input. So the amp can mate with a giant preamp to take at least 4 Volt out to drive the amp. I am thinking to put gain stage(s) in the input of the amp. So the question is if I add gain stage(s) to the amp, does it mean the input voltage of the amp will reduce below 4 Volts?

Yes, adding a gain stage at the input would reduce the voltage needed. How much less voltage depends on the amount of gain that you add.

To get to a 1 volt level you will need to add 12db, which is easy with most tubes that might be in a gain stage.