With the rear wheel correctly aligned there is only a 3mm or 4mm gap between the drive belt and the tyre sidewall. Not much chance of going up from a 175/65-15 without clearance problems. I did see a 185 sticky Avon fitted to the rear on the ex-factory racer M3W when "Hugo" had it but it had a misaligned the rear wheel to get the clearance. Once it was pointing along the middle of the car, rather than the RH side, the tyre touched the belt. When it was sorted the steering wheel position needed altering to center it.