Just found the E53 option code. JCL was correct. The option code increases tow capacity to 3500kg (7,700lbs) with a 12% gradient maximum. Actually, the standard towing capacity is also rated at a 12% gradient maximum. The increased towing capacity option was available for the V8 and I6 Diesel cars so I think it's now safe to say that concern here is power rather than chassis strength. As far as the chassis and suspension goes, it looks like the E53 is actually good for 7,700lbs per the manufacturer.
JCL, any input?
See below:
http://www.bmw.be/be/fr/newvehicles/..._datasheet.pdf