I would agree with increasing squat frequency, but not to every day (yet). Eventually sure, you should be able to do that, but you're so not used to it that trying that now would wreck you.
Also, look at the guidelines for Thibaudeau's HF strength work--they take a lot of principles in common with Oly guidelines for loading: a) a daily "max" isn't a true max, it is the max you can handle WITHOUT 1) technique breakdown 2) slow grinding of the rep (must be smooth and powerful) and/or 3) no mental psyching up.
Basically when you squat daily or near daily you do much much more submaximal work in PL terms, at least in the beginning as you're getting used to it. You go up in weight only until technique breakdown or speed breakdown.
So when you increase squat frequency consider that as guidelines for loading parameters.