On a car that old, pretty much everything is suspect. Shocks you say are new, but did you use the good ones (Bilstein)? Time to start inspecting suspension items. Rubber parts are probably not in good shape if they're original. Sway bar end links are another thing to look at. Spring failures are less common, but have occurred. A broken sway bar (or two) is another unlikely but possible thing.

These aren't sports cars, but when properly sorted they do handle much better than most American cars of that era.

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Whoever said there's nothing more expensive than a cheap Mercedes never had a cheap Jaguar.

83 300D Turbo with manual conversion, early W126 vented front rotors and H4 headlights 401,xxx miles
08 Suzuki GSX-R600 M4 Slip-on 26,xxx miles
88 Jaguar XJS V12 94,xxx miles. Work in progress.
99 Mazda Miata 183,xxx miles.