Parasound a21 upgrades

a common approach for sure but until you try one you will not understand the impact a preamp with gain stage has on overall sound.  
your amp is not at its full potential until it receives a powerful, dynamic signal which requires gain.  
having had several amps and preamps as well as integrated amps with passive preamps, a quality preamp can literally wake up a sleepy sounding amp.  it is much more than a source switcher.  
even though the a21 is not balanced, it will take advantage of balanced preamps which offer more gain with lower noise.  
this is the best way to take your system to a much higher level even though your direction is a different approach currently.  

I was in the same boat.  I had both A21 and several JC1.  The A21 has 5 fuses that affect sound quality (1 on back panel and 4 internal).  I could never get the amp to sound good regardless of what fuse I tried because it deviated too much.  You could try Audiomagic Super Fuse (which is almost a better version of stock).

A power cord upgrade is good.  Other than that, you are better off switching to a different amp like others have suggested.

re, preamps, especially a tube based preamp.  
power cords did zero for my a21, two made the sound worse.  

Thanks for the suggestions. I think I will take Eric's advice and leave it alone. I do really like the amp. Added dedicated 20a circuits today. Nice improvement! 

If you haven't already, you might try some vibration control.  Just three Stillpoints minis, for example, will provide a very significant sonic improvement.  And then you can go down that rabbit hole instead of spending more on a new amp :)