If the 1M does indeed have similar/the same suspension as the M3, you can go up to 265-275 front, 285-295 rear. You would obviously need wider rims to fully utilize the wider contact patch. As for overall diameter don't worry about it too much. BMW's DSC is designed to be pretty tolerable. (I have 265/35/18 and 295/30/18 which is way off of stock)
As for tires for street extreme performance you can get Yokohama AD08, Bridgestone RE-11, etc. For DOT-R, Michelin Cups, Nitto NT01.
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