There's a lot of conjecture and speculation on the multiple quench, going many different directions. Personally, I believe in it, not simply by doing it for a number of years, but through spectrograph testing of many, many samples. BUT! Here is the caveat.....
Based on the testing I've had done on numerous samples, everything points to it being effective on steels that posses .060-5.0% chromium. I chose to focus on 5160 and 52100 and how the multiple quench relates to/effects those steels. I've not used O1 in a long time, but did send a few multiple quenched samples in for testings. Looking at those results, although the steel showed a slight grain improvement between one quench and two, at 3 quenches the grain in O1 was essentially right back to what it was with a single quench. The one thing that caused me to stop chasing multiple quenches on O1 was the fact that differentially hardening it was hit-n-miss at best, and the ability to control the depth of hardening was a major aspect in my pursuing multiple quenching.
5160 and 52100 results showed improvement up through 3X quenches, then started to go the other way. Even with those two steels there are a lot of nuances that can "make or break" it.....it's much more complicated then just bringing the blade up to it's recommended critical temp and quenching. Variations occur with the austinizing heat you utilize, it's duration, and of course the quenchant used. Deriving the maximum benefit from multiple quenching takes a lot of time, effort, and experimentation.
I suspect there will be a number who will read this post and shout "hogwash!".....and that's OK. I achieved my JS, my MS, and have a number of cutting competition 1st place finishes under my belt utilizing multiple quench techniques that I have learned and honed over the years. I don't set back and say "that's good enough" either......I continually seek to better control, and improve results utilizing multiple quench techniques. Do I use it on everything? Of course not. Generally only on the two steel types I mentioned, simply because those are the ones that I know benefit from it versus a full single quench on the same steels.
As with most everything in knifemaking, it's impossible to provide "empirical evidence" that something "works" or doesn't. Were we in a perfect world, where there were no variables from shop to shop, and maker to maker, it MIGHT be possible.... and in SOME instances we can "get close", but after being in this game for all the years that I have, the one constant is that there are as many ways to do something, as there are people doing it. Only through a lot of time and experimentation do people gain enough knowledge/experience to be confident/comfortable with their results. I say that because over the last few years, it seems that everybody is seeking that "magic bullet"......wanting it "right now", and being unwilling to take the time and effort required to "learn".
Over the years I've had many "discussions" with many makers about multiple quenches....some receptive to it, others not. In most cases it boils down to a matter of opinion, and the tenacity to seek improvement each day you walk into the shop.