What is the range of offset that can fit on a Mini? Would a 16x7.5 offset 38 work?

 

I am running 38 offset with 15s . Currently running 205/55 and upgrading soon to 225/50. No problems here.

 

Compared to stock 16" wheels and tires-

16x7.5" with +38mm offset will be OK. About +36 to +40 mm offset in that width will work if you use tires of about stock tire diameter or less for best clearance.

Trouble comes from lowered suspension which can reduce clearance in the rear. Once rims get wider than about 7.5" then offsets of +40 to +45mm risk rubbing on the rear lower trailing arm so either spacers are needed or offsets of about +36mm or less.

Best tire size for you would be 205/50-16 which fits 16x7.5" rims or
225/50-16 but with stock suspension (it's taller than stock at 24.7")

 

I'm running 16 x 7.5 OZ Ultraleggera's (ET 37) with 205/50/16 non-runflats. No clearance problems.