There have been several threads concerning oil consumption very similar to what you are experiencing. As posted, BMW states a quart per 1000 miles is acceptable usage. I can't buy into that and would be looking for a problem as you are doing.

Of the suggestions, I would start with reading the plugs and checking compression before trying heavier weight oil. If it is time for an oil change I might try 5-40 oil though I think that is masking a problem. IMO using a quart per 1000 miles is going to increase maintenance and be a negative impact on plugs, valves, o2 sensors, cats, muffler, etc.

Of the potential causes, CCV trumps all others in previous threads.

If you are using a brand that meets BMW specs I don't think changing brands matters. Most of us have a particular brand we feel is the best but just because someone uses a different brand and uses less oil does not mean the oil is making the difference.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas