I've done tried completely different size as well as compounds of tires front to back since the mid 90's after I got my first car 1995 Honda del Sol VTEC and took it to autox as well as rr. It works well for low speed autox but the grip differential was a bit too much for high speed stuff. Could've tried more different setups but I was on a super budget... anyway, just saw this clip above and they used different compounds between left and right side. Very cool. Just goes to show you do whatever it takes to win. And don't listen to the haters and nay-sayers and experiment and think creatively...

 

it all comes down to tire temps in the end