You could easily upgrade to 17 inch wheels with 225/45/17 and 255/40/17 tires,the choice is really good ... Dunlop Dirrezzas,Bridgestone RE11's and perhaps loosen up the rear swaybars to dial out oversteer.I would think you have too much of some stuff and not enough of other things like brake pads and rubber ... then again driver could use some work as well
More rubber contact is always good !
Cheers
Phil