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325x30-21 with 285x35-21 is what I'm researching in a 21. For 20s the choices are more numerous, running 315x35-20 with 275x40-20. You pretty much have to pick the rubber first then find a rim that works with it. Going stock size or non staggered will be the easiest to fit no doubt.
Vossen makes a 20x9 et32 and a 20x10.5 et30 that looks promising for the 20" fit. Stock flushness to the fender would require 20x9.5 et31ish and a 20x11 et29ish. (I'm confident the vossen solution will work although al of the extra width vs stock is under the car)
SSR 3 piece makes 21x11.5 et25 and a 21x10 et24. (these would be 10mm further out than stock, and about 20mm further in behind the wheel as well) Stock flushness to the fender would require 21x10 et36ish and 21x11.5 et34ish.
Rolling diameters are about a half in shorter though, in both staggered builds, and the 21 s are mostly run flats.
There is lots of room behind the wheel luckily to go wider, but I have not measured if this will work yet. Its a full 30mm closer on the backside to keep the front side equal to stock flushness. In actuality the wheels can be pushed a bit more out, freeing up clearance on the backside, and making the flushness fit more aggressive. (without rubbing, or poking) Knowing where stock is makes an easy adjustment to add some offset to the numbers above.)
275x40-21 non staggered might be a great fit too, but now the offset between front and rear is quite large for rim selection. Maybe get the same wheels and just run a spacer in the back. Allows for tire rotation.
This is just early research though, so no real great fits are measured yet. In the ballpark though. The BMW X5/6 Ms run the tire setups, so the tires do exist in the above setups. Bolt circles are different though and offsets.
So stock, or staggered X5/6 M sizes, or non staggered in a 275 are about the best case scenario for rubber. Next step is getting the rims dialled in.
in22s there are 285x30-22 and 335x25-22 (thats 4 sizes bigger in the back, so fit might be problematic at this point, but it might fit once measured up)
To go non staggered, you need a 22mm rear spacer to match the stance to the fronts. for example a winter setup. 265x50-19 SP Winter Sport 3D tires on all 4 corners. 19x9 et30 OZ Monaco HLT on all 4 corners. add 22mm spacer in the rears. stock is et26 so 4mm more tucked than stock. less road salt fling.