Drove a 2011 Cayman R for the first time.

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Stephan is right on about car dynamics. Learning car control skills is a lot like learning any sport. It takes practice.

I have driven both the Cay R and Box Spyder with PDK and they felt pretty good to me for a stock car (same chassis). Tires and alignment matter as well. Eyeballing your pic it looks like the Cay R has no negative camber in the front which would make it prone to significant plowing. My first stop would be a performance alignment shop.