Minivan taxis definitely exist here but they are not all that common. If you want one specfically, you may be able to get one by calling one of the bigger cab companies and putting in a request - although I am not sure if they can honor it. If you are at OHare and waiting in the queue, you can let the person who is herding you into the cabs know and they will have you wait on the side until one comes along that fits your criteria.