Since the car is new to you, I'd go with the alignment/suspension components/tires reasons for high speed handling issues. Maybe worth having a look there.
The Boxster is fairly new to me also, and takes a little getting used to as far as how fast you can corner and how hard you can accelerate midway thru a corner (full throttle!). Very impressive! I used to roadrace motorcycles way back in the day, and what the older Boxsters lack in power they can make up for in late braking, cornering speeds and line changes. It's fun to crank the wheel hard into a hairpin turn and feel how balanced it is when it breaks traction. Very forgiving for spirited street driving.
~M
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