Having personal experience with Parasound A21, I will say that the Parasound sonic signature is definitely on the warm side of things. It is a very good amp and has a very refined midrange sound, but still on the warm side.
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Parasound uses excellent parts and components and they have an excellent overall design. I have found that the one thing that holds back the Parasound is how many fuses it has. Parasound likes to fuse the heck out of their amplifiers. The A21 has 5 fuses total.
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You can make the Parasound A21 a world class amp by just investing a little more into fuse upgrade:
1 x Hi-Fi Tuning Supreme LARGE 15A for the back panel main fuse.
4 x Furutech LARGE 10A for the internal post-transformer fuses.
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When using Furutech for all 5 fuses, the sound was still excellent (much better than stock), but was still too warm for me (I lost resolution and attack). The single Hi-Fi Tuning Supreme silver fuse boosted the speed just enough so that I had excellent attack / resolution / detail.
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However, in your case, with the older 803S that uses the aluminum tweeters and the older kevlar midrange breakup issue, you might want to try out all Furutech first. 400-500 hours of burn-in required for Furutech before you should make a decision.
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The older kevlar midrange had an issue with break-up which caused distortion in the sound and could come across as too bright/harsh in some systems. A slightly warmer amp can mask this problem as well as the bright/breakup of the aluminum dome tweeter.