Sounds like a pretty big tire mismatch and I would expect the car to snap oversteer easily. Mixing tires is fine as long as they are very similar in grip and responsiveness. Ps2 and Sumi are quite different which is why your car is so twitchy. Go with the same tires on all 4 and it doesn't matter which brand you choose.
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2009 Cayman 2.9L PDK (with a few tweaks)
PCA-GPX Chief Driving Instructor-Ret.
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