'87 560SEL Handling characteristics

Anyone out there have comments on how to tighten up the high speed handling of this model? (80-120 mph). I know it's not a sports car, but the "lag" time before the car takes a "set" is disturbing and after driving the car thru mountain terrain and quick L.A. freeway tours on my vacation last week, I have to say I had to really work at being smooth in this car. I have many years of roadracing experience in both fast touring cars and single seater formula cars. I expected more competence in this sedan in it's handling capability. Will a roll stiffness increase alone be sufficient, or am I looking at also increasing the tire contact patch area and upgraded shock/dampers?. Any comment(s) appreciated.

Thanks, Mike McLaughlin