I had very bad vibration on my m3p when I collected it 2 Decembers ago. My hands would be buzzing after driving. Like white finger. It went back to tesla twice, for 1 week at a time for thorough diagnostics. They acknowledged the vibration, but when they couldn't fix it, they eventually told me its as per design. I was in the process of handing the car back with the finance company when I decided to have one last shot at resolving it. I took it to my local wheel shop. Skidz, in Falkirk whom were very quick to tell me they just hadn't balanced the wheels right. They countered balanced them and added twice as much weight to that of the service report. I measured their crappy weight tapes when I got home, that's how I know
Anyway, Skidz fixed it. Problem gone. Moral of the story, Tesla can't balance wheels for toffee.