Does amp output V decrease by adding gain stage?

My tube amplifier is low sensitivity, has high output voltage at 4V. I plan to add one or two gain stages to improve the amp sensitivity. The question is by adding gain stages will that results in lowering output voltage?
Increasing gain in the input voltage amplifier stages will increase input sensitivity but should have no effect on the capabilities of the output stage.

But a 4V output for an amplifier is very, very low. Perhaps you are talking about a preamp?
4V output is low for a preamp too.
I made a terrible mistake. The INPUT voltage is 4 voltage. Very insensitive amps I got to say
So what is your question then?
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.