Since about 2010 I have been using AMSOIL Signature Series ATF Fluid in my E46 330Xi and since 2014 in my E53 4.4i without any issues.
https://www.amsoil.com/shop/by-produ...ullDescription
I did a multi drain and fill 4X on the E53 to insure that I got all or most of the 80K mile fluid out of the beast.
https://www.amsoil.com/lit/databulletins/g3110.pdf
Full synthetic rated to meet Dexron III specs.
In conjunction with changing a couple of solenoids (to solve a nagging cold slippage transmission issue that has baffled me for several years) in the E46 just recently, I did a drain and fill of about 6.5 qts and filter change and was lucky to find the AMSOIL fluid on sale at Farm & Fleet for $6/qt.
Mike