Need help with tire dimensions

Hello there, been on e46 fanatics for a while and this is the first time i need help. My grandparents have a 99 328i and needed to get the tires replaced again. They were last replaced in the beggining of Jan of 2007 when i wasn't in spain. Now they need to be replaced because the car needs to pass inspection but the tires are bald. They for some reason have aftermarket Momo gt-r 17inch rims but don't know the dimensions of the rims. . They are running Michelin pilot sport tires with 225/45zr 17 91y in the front and 225/45zr 17 94w in the back. The fender has not been rolled and it doesn't rub with the sport suspension. Problem is, can i go wider in the back because we have been having problems with the stretched tire in the back falling off the rim. If i go wider, how wide before rubbing? Changing rims is not an option. Pics at the bottom. If you need more pics, please let me know. front
rear (both)

Looks like you could run 235 or maybe even a 245.

so like 235/45 or even 245/45 ?

Keep in mind, its by 10mm's. and it looks like youre at stock height, so the 45' is jus a ratio of the width, i.e. 225/235, so that doesnt matter too much. youre best bet would be to dismount, and hope that theyres some engravings on the back, for the exact width. it looks like youre already wide for the rim though, so i'd say 235 would be what i'd go with.

Thank you so much for your answer. I will keep in mind about the markings when i go to get tires tomorrow.