When I was a student, some known enzymes had a catalytic efficiency higher than the theoretical maximum (i.e. they were faster than kinetically perfect enzymes.

This has since been resolved by refining the model of substrate diffusion, but for years (decades?), it meant that some enzymes were using a mechanism that had not yet been discovered.

Edit: I just looked it up, and it appears at least one enzyme has exploited quantum tunnelling to achieve these impossiby-high production rates. That was taught to us as a fringe theory when I was a student.