My impression is that multiple quenching refines the grain structure of the steel which both toughens it and makes it take a sharper edge. Ed Caffrey really works on the multiple quench process. Below is a quote from a previous thread:
"Although I have not tested all the steels with a multiple quench (and most likely never will), I have found that those steels that possess a mild to moderate (moderate meaning not more than 5%) Cr. content respond very well to this type of process. There are a couple of very simple steps that actually serve to enhance grain structure during the multiple quench process. When I first started this process on my cutlery, I thought that the steel was getting "softer" after each quench cycle, but after having several samples spectrographed, I discovered that the grain was being refined with each successive quench cycle.....up to general number of quench cycles. I can't present you with undisputable scientific proof, but I certainly believe in it. During these tests I was so certain that there was something major, that I was either doing right, or wrong, and only when the spectrograph results came in, did I realize that in knifemaking, it is more often than not the "little" steps that make either monumental improvements, or heartbreaking failures."