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When we looked at the demo there was a suspension part real close to the front tire at the top. I mean REALLY close. No way you could put chains on. So I'd take a look at that before trying bigger tires!
Bigger tires as in more side wall? If you want wider, 225/50/17 look like they have the same rolling dimensions, but not sure if they would be too wide for the vehicle.
The 225/50/17 is the same diameter as the 205/55/17 it is the same width as the 18" option. This is a widely available size and should fit the Countryman like a glove. I will switch to this size as soon as the OEs run out of tread.