w140 with SPS
Can the power steering be damaged if turned with pump not running?
Turned more than a few times that is... don't know how many turns and for how long.

So is it possible to damage the steering box?

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85 190E 2.3(SOLD)
86 230E (-->300D) sold
87 300D (-->300TD) sold
68 250S w/ a 615 and manual tranny (RIP)
87 300TD (SOLD)
95 S280 "The KRAKEN" (Turbo 2.9 602 transplant) traded
86 190E 2.3... current project

Generally no, for one specific poorly designed car yes.

When the wheel is turned, fluid is displaced from the steering rack / box and it ends up in the pump reservoir. If there is an overfill situation or a low free space reservoir, fluid can be displaced out the vent. My 1984 Ford Bronco will dump fluid if I turned the wheel with the engine off.

The specific car I've seen damage occur was on a 1997 ish Pontiac Grand Prix, these used a sealed power steering cap and this particular car may of had an over filled condition. The drive belt broke, car was driven, power steering return hose popped off the barb. ( these are attached with a hose clamp since it is a no pressure return hose. )

If you car has a non vented system, I'd open the cap to release pressure and then once the engine had run / shut off, open int again to release vacuum.

I drove my '77 240D from San Diego to Carson city with no power steering belt once. No damage.

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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.

As a side note, if you have to drive without the PS pump turning, drain the fluid out. This way you are not displacing fluid every time you turn the wheel.