Play in the steering wheel is usually the gear box. It also could be in the steering linkage: tierods, center link or idler arm bushings.

While causing drivability problems suspension play; ball joints, control arm bushings, etc. does not usually cause steering wheel play.

Steering gearboxes are supposed to be adjusted off the car. Many experienced techs can do a decent job on the car but its not easy on the 420s as the exhaust is right over the adjustment.

If you haven't already, you should find yourself a good technician to evaluate this and future situations. I wouldn't recommend a tire store for this. My personal recommendation is an independent specializing in MB that does their own alignment.

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Steve Brotherton
Owner 24 bay BSC
Bosch Master, ASE master L1
26 years MB technician