I had a 318iS and went from 15" to 17" alpinas with 225/45s on the front and 245/40s on the rear.
When I was shopping around I had all manor of conflicting advice. I did hear that the larger wheels can be a prob for 316s due to the size of rubber on the floor that requires moving and the engine power but have to say that I wouldnt have thought that would matter too much.
Most places that do tyre and wheel packages were going on 215/45s but then again thats what they sell em as.
I didnt consider dropping the car but was advised by a bm mechanic that there would be room, how much I'd ask someone like BMW world in Milton Keynes or a dealer.
Have to say that I did notice a marked 'tramline' effect on very uneven roads but the difference in grip and looks was superb.
John