must be a good reason i've never heard of this but here goes.

due to circumstances beyond my control, i had mismatched tread on the front tires of my vette. this resulted in some highway shake at 70 mph. (resonance of some sort) but it also made the car less tail happy to the point where i would consider my handling nearly neutral now whereas before it was a moderate oversteer.

is there a reason why one couldnt (or shouldn't) alter the handling balance of a FWD or AWD car away from understeer by using mismatched tread on the rears?

 

There are a handful of reasons not to mix tires on that car let alone any other car. Main problem is giving the car a split personality in handling and traction. In inclement weather your going to be treading debris differently from front to rear. The tread pattern and compounds will be different and this will effect how water, snow/ice etc is pushed away from the car. It would be like shoveling your driveway with a work boot on one foot and a dress shoe on another.

Another is handling. If the speed ratings, compounds, internal construction, or even tread depth is different on each end of the car its going to drive differently. A lower speed rating in the rear may give the car a better chance of over steer due to its less internal construction for example.

In short, its just best to have all four corners match. Its even more important in sport based cars where tires are a vital part in the vehicle performance.