Heavy is a relative term not only in actual weight but in percentage of weight. Even the most "gassed" up WPO lifter would not try to squat with heavy percentage weights 2 times per week and they recover faster than any of us here. You are running the risk of injury and over-training especially if you include assistance work.
He could, but I sure wouldnt recommend it. When you say "heavy squatting" that leads me to believe that you are working in a high percent of your max. Twice a week, nevermind 3 times, is too much. Lets hope you dont plan to deadlift in that same week. If you are looking to squat twice a week, do like Vaughn says, one max effort, one speed day.
Although others think it's possible:
So in my opinion if by heavy he means 90%+ twice a week I'd say no way.
That's what he asked, the answer is definitely yes, although there is no reason not to use supplements.... Now I don't have good physiological knowledge of the CNS, I just know what I did and that it worked, it was a bit difficult a first but you adapt. What Todd is pointing out is that maybe people should think outside the box here, if you have always been squatting twice a week, that's what you have adapted to but that doesn't mean you cannot adapt to something more
It's simply a matter of adapting to increased training tonnage. The human body can adapt to this just as it does anything else.