A Mercedes is really not the best choice if you want a 'stiff' ride. Still, you can have a soft ride and still corner flat. Our W201 has a much softer ride than our Honda Accord, but does not lean any more in the turns, and handling is comparable.
Shocks, of course, will have little effect on lean in turns. I would check the plastic links on the rear sway-bar, and replacing the sway-bar bushings front and rear will probably also improve transition response. On ours, replacing just the front bushings made a surprising improvement in straight-line tracking, particularly in windy conditions. This even though the old bushings did not appear particularly worn-out. Handling in turns was fine before and after.
Check too for the condition of the rear suspension links. The rear wheels should feel rock-solid when shaking them around by hand with all four on the ground.