The passenger high beam and driver low beam are all that work and they will even be on together at the same time which is not suppose to happen.
I have a 07' cooper S that I have had for about a year and recently had the headlights have started to go out. On by one high or low beams on each side would cease to work, so I replaced the bulbs. Unfortunately I found it made no change to my issue. I did notice that the casing on the wires to the bulb's socket/plug were crumbing off. So I got new connectors and with some help I spliced them in as far back on the old wires as possible. This made a marked improvement, going from 1 out of 4 beams to 3 out of 4. All active lights working as intended But I still had that one passenger side low beam that refused to cooperate. We checked the fuse box in the passenger foot well and tested our own handywork with a voltmeter found no issues. Since then I have also lost the driver side high beam. However this time with a twist. When lows are on and I switch to highs. Instead of the low beam turning off and the high beam coming on. The low beam stays and the high beam joins. This should not be happening and is a recent development that came about a week after we did the wire fix.
I have no idea what is happening, my friend's best guess is a module issue but neither of us our sure.
Sorry for the long post. would appreciate any help.

 

Do some searching on here for the FRM module, or footwell module. It's a decent culprit but I don't think your symptoms exactly match what most people experience. For me personally the low beams were always on whenever the car was running, no response to switch or high beam command, and two power windows stopped working.

EDIT: just noticed your other post, can't delete this entry, sorry.