It is possible to put bigger/smaller rims on cars, because the size in inches changes from car to car, e.g. the Honda civic level 3 rims are 19", the Mazda rx7 level 3 are 20", etc.
Install the rims you like on the car you have. Then, trade your car in for a car that has rims of that level bigger or smaller than your car. Return to the rim customization screen and pick the same rims on that car. Although they already are installed, you must reinstall them for the game to register the size change. Clicking on next will simply ask you if you want to install the rims, although they already are, say yes. Then, go and trade your car back for what you had and it will keep the rim size you put on. On some cars, bigger rims will make them go through the fenders.