I agree with earlier posters that there are a number of factors affecting the sound of amps, including the speaker load, how loud you listen, and a vast number of factors in the amp design itself. And you have to remember that most Class AB amps run full Class A until they reach a certain output level when they begin switching into Class AB, and then further up the output curve they switch into Class B. If you have sensitive speakers and/or easy loads, your current amp (no pun intended) may already be running in Class A.
The old Class A dreadnaughts of which the Krell KSA series is one, along with Mark Levinson, Threshold, NRG Control, and others were primarily designed to run Class A into low sensitivity speakers with difficult loads like some Thiels and planar and ribbon speakers like Apogees and SoundLabs. Nelson Pass of Threshold and now Pass Labs says you can really tell whether an amp is running true Class A by its weight as the required massive transformers and heatsinks weigh a lot. As previously stated, Class A amps have all of their output devices running full-out all the time and divert all output into heat and the speaker load. As the volume output increases they divert more of the current into the speaker load and less into heat. However, these monster amps may not have necessarily sounded the best, especially when they were only outputting small amounts into the speaker load and mostly into heat.
IMO, the use of Class A does not always guarantee the best sound, especially since "sound" is largely subjective. Perhaps if you have a difficult load this might be true more times than not, but if it were me I would listen to some different designs with good reputations like those mentioned previously. I use some esoteric equipment by Essence that came in Class A and Class AB designs and I liked the Class AB presentation better. The Class A monoblocks used a more massive power supply and the sound was more robust and had more bass weight. The Class AB stereo amp was much faster, transparent, and had a more prominent and extended treble, which was a better match with my speakers.
Good luck.