My first guess (considering the mileage) would be loose or worn suspension components. The added load on the rear puts added stress to those components, and things start to get loose when driving at high speeds.

I'm not an expert at what to look for, but check the rear crossmembers bushings for signs of wear.

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car