The stock Goodyear Eagle RSA tires are, uh, well, lousy at best. A good set of summer performance tires will make a huge difference in ANY vehicle's handling.
There are a few of us who have taken our PTs out on road course days as part of the NASA HPDE series (
www.nasaproracing.com) and always surprise the heck out of other participants, so the PT can be made to handle reasonably well. Keep in mind that no matter what you do to it, it will always be a FWD, high center of gravity, 3300lb car. None of that adds up to truly great handling.