Over inflated tires do not handle BETTER. There is a point where performance drops off, and the tire starts to feel greasy and actually loses grip.
More air pressure can make a tire FEEL more responsive to steering inputs, but that doesn't mean more absolute grip. Some very stiff high performance tires actually work better at lower pressures on light weight cars.
The TOYO R888 DOT competition tire, for example, recommends a HOT pressure of 32 - 38 psi. That means a cold starting pressure of as low as 25 - 28 psi. This is, however, a VERY STIFF tire.