can you alter the gain of an amplifier?

Perhaps in some cases, but I wouldn’t recommend it without first giving the designer/manufacturer some idea of how much you want to increase the gain, and getting his or her blessing.

For example, if the solid state amp uses a considerable amount of feedback, it may be possible to increase the gain simply by changing a resistor in each channel. However, doing that would to some degree increase total harmonic distortion, lower damping factor, increase output impedance, and affect sonics for those and other reasons.

In extreme cases increasing the gain of an amp might also change it into an oscillator, possibly resulting in damage to it and/or the speakers.  The possibility of oscillations would depend in part on the impedance characteristics of the particular speakers that are being used, so the modified amp could conceivably work fine for the tech but blow up in your application.

Basically, increasing the gain amounts to incorporating a design change, which should not be done without complete information and full understanding of the specifics of the existing design.

Regards,
-- Al

I agree with Almarg.
Now, I do have a Crown amp that does have a 3-position switch that can change the gain of the amp to 3 different settings - 0.7V for max output power (which has gain=32dB), 1.4V for max output power (which has gain=34dB) & a fixed 26dB gain (which has a sensitivity of 3.1V for max output power).
In this case I was lucky that i can change the gain without much fuss.
If such a switch is not provided then changing the gain is much more complicated & will have effects on many performance parameters like Almarg cited.

Well... you have made decisions which, imo, make it more difficult to achieve superior sound. By insisting upon using volume control in sources, i.e. CDP, you are locking yourself out of potentially far superior systems. You may have had success in using CDP as source and preamp function, but I found in many iterations with very fine CDP's that one can obtain far better sound by doing two things; use the CDP as transport and get an outboard DAC, and use a passive or active preamp with it. You are in no way assured to have superior sound simply because you are using the volume control of the CDP and the CDP's DAC. 

You may lose a touch of the most extreme refinement/cleanness going this route, but you will have an overall far higher end result in terms of most other parameters of fine playback. Trying to futz with amps is not a good solution, imo, and you will still have a largely compromised (not fully realized) system.  :) 

Adjustable gain in amp is very helpful to synergise with preamp or any input source with volume control.