Sounds like your 22's are 8-9" wide. I posted a link below for reps which are 20" x 10-1/2" rear and 8-1/2" up front. The rear would run a 315 which is plenty wide. These reps run around $800.00 as most do. You will spend 3-4k for new oem wheels.

4 20" x5 Y Spoke Matt Black Style Wheels Fits BMW x5 2000 Present 3 0i 4 8i | eBay

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2001 E53 4.4 Alpine White, Sports Package
2000 E36/7 2.8 5 speed Bright Red w/ a HT!