You mean overvolt your fans? It'll wear out the fans faster, generally will create disproportionally more noise, and possibly burn out a motherboard header (if you used that instead of a direct molex connection), but it's possible.
Basically it'd take some rewiring to the point where you'd just have a simplified controller (minus the actual ability to adjust the voltage on-the-fly). So if you don't have any experience or equipment doing electrical work, it'd probably be just as expensive (sodering iron, soder, etc.) and far more troublesome than buying a controller capable of doing it (although I didn't know that there are pre-made controllers out there that allow overvolting).
I'd personally suggest just getting new fans.
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