The most common cause of come and go wheel shimmy is the inner vs. forward control arms.

If you get wheel shake when you gentle brake at 45 ish mph or if you get steering wheel wobble when you steer left and right past center at 60-70 mph it's almost certainly the case

I had a similar come and go shimmy that turned out to be a bearing but that was much more subtle.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)