It is possible to replace the diaphragm in the booster but you probably will not be able to purchase the diaphragm by itself and will probably have to replace the booster as a unit ;(

I'm not sure what you mean by "pump" does E70 have a dedicated vacuum pump for the brake booster ? Regardless, the way you are describing the problem I would bet dollars to donuts the diaphragm is ruptured.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)