Just remove the alternator, take the bolts out, rotate the alternator and pull it towards the radiator. It comes out pretty easily.

That will give you all the room you need. There is no room to move the alternator out of the way without pulling it out since it resides in what's basically a hole.

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Current Bimmer
2004 X5 4.4i Sterling Grey Sport/Premium

Past Bimmers
1991 318I Alpine White
1995 740I Alpine White
1991 525I Schwartz
1998 323IS Scwartz
2004 330CI Cabrio Titanium Silver Metallic
1995 540I Schwartz
2000 Z4 3.0 Titanium Silver
2000 330ci Coupe Titanium Silver