I wouldn't add an M badge to a base model myself, but there are lots of M Sport versions around, including of the X3, since about 2005. They get M badges on each wheel, the door sills, the dead pedal, the steering wheel, the gearshift knob, the instrument panel...etc, as well as some aero mods. Other models beyond the X3 get M Sport suspensions, and so on.

M stands for marketing, not magic, IMO.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue