I've actually transported four stock rims and tires in the crossfire before. You may have a hard time transporting four rims in the boxes...but if you take them out and wrap them in blankets you should be able to fit two in the back and you may be able to leave the other two in their boxes to fit in the front seat.

When I had to move my four rims and tires I put the two 18" rims in the back and shut the hatch gently. Then I put a towel down and stood the two 19" rims up in the front seat. They fit in their, very little manipulation needed. Just an arm to hold them in while you are driving so they don't spill over into the drivers seat.