[Keenercarguy]

I agree with mistersheep (sell the old rears) but,
I run Michelin Pilot Supersports in the front, and Dunlop Direzza DZ102's in the back. The DZ102's have moderately less grip than the Super sports: but they're not bad by any measure. They also have a much higher treadwear (460 vs 340) and last noticeably longer without sacrificing much grip. Best part is that the handling characteristics are perfect. Granted I'm also fairly modified suspension wise...
I'd DEFINITELY run a better tire up front if you're at all comfortbale correcting oversteer in that super unlikely scenario that it occurs. I'd say it's also much more important to be able to steer, if you're going to run a lower performance tire somewhere, don't put it on the wheels that are the difference between hitting that deer or weaving around it. All IMHO