In an approved oil, GC would be the one.
Castrol Edge (RS) may be available if you look.
https://bobistheoilguy.com/forums/threads/castrol-edge-0w-40-6200-miles-00-e46-330ci.95036/
M54 block, and has done ~63000 miles.
Ive owned the car since 46000 miles and it has a FBMWSH.
2 reports here. On the 2nd sample of oil, i had done 1 track day back in June. Engine mods include 3rd cold air feed, and muffler delete. Running Shell V-Power (99 RON Gas), averaging about 26-27mpg. (Ive put the universal avergaes in brackets)
Miles on oil=======7046----------------6260
Total miles========56845-------------63150
Date==============05/08/08---------09/26/08
Make up oil=========1.5L--------------1.75L
Oil Brand------Castrol RS Sport----Castrol Edge
Grade---------------0W/40-------------0W/40
ALUMINUM-------------3-----------------4-------(3)
CHROMIUM-------------0-----------------0 -------(0)
IRON------------------23----------------29 ------(11)
COPPER---------------10----------------7 -------(7)
LEAD-----------------14----------------25 -------(5)
TIN--------------------0-----------------0 -------(1)
MOLYBDENUM--------4-----------------131 ----(88)
NICKEL----------------0-----------------0 -------(0)
MANGANESE-----------2-----------------1 --------(1)
SILVER----------------0-----------------0 -------(0)
TITANIUM-------------0-----------------0 -------(0)
POTASSIUM------------2-----------------1 -------(2)
BORON-----------------4-----------------53 ----(57)
SILICON---------------6-----------------4 -------(4)
SODIUM----------------2-----------------3 -------(5)
CALCIUM-------------2953-------------1817 ----(2500)
MAGNESIUM----------160--------------25 ------(89)
PHOSPHORUS---------850--------------722---- (810)
ZINC-----------------1212-------------880---- (989)
BARIUM----------------0-----------------0 -------(0)
SUS @ 210F----------71.9--------------69.1
cSt @ 100C----------13.45-------------12.72
Flashpoint F---------375---------------405
Fuel %----------------0.5-------------- Antifreeze %----------0-----------------0
Water %---------------0-----------------0
Insolubles %---------0.5----------------0.4
The report from May was as follows:
Iron and lead both read high in the initial sample from your engine. These metals mainly show
bearing wear, though iron can come from any steel part. Both are fairly high for an oil run 7,046 miles, but
not cautionary. Since everything else looks okay, we are not ready to call these results a problem just yet.
The universal averages column shows typical wear from this type of engine after 6,400 miles on the oil. A
little gas was found, but not enough to cause the excess wear. Try 5K miles next. You could also change oil
types, though usually brand doesn't matter.
The latest report from last week:
Oil usage decreased but iron and lead both increased and that is not a good sign. The iron is
coming from steel parts like cylinders, the valve train or rotating shafts. The lead is coming from the
bearings. Both are at cautionary levels indicating excessive wear. Their rate of wear (ppm/mile) also
increased and that shows a mechanical issue inside your engine. No gas, moisture or coolant was found
plus air and oil filtration were normal. All five can be ruled out as factors in this high wear. Track days can
be a factor. Shorten oil runs. This is a Caution report.
I'd be using a 50 weight.
Consider Shell Rotella T Synthetic 5w-40, just don't tell anyone.
Another unspeced oil would be Mobil 1 10w-40 HIGH MILES.
I just let the dealer do my free oil change and either drain it when I get home or run it for a while and then install my own oil. If they use BMW 5w30, I'd get the free service for winter then substitute a thick oil for summer.