Not sure about Cox but they may charge you to have an extra cable box. I would suggest calling them and see what the price will be. IT might be an extra account charge or they may allow a certain amount of boxes in a house with no or small charge. Just don't go and buy a cable box before you call them or the person that has the account will have to talk to them to get it setup. The account might be setup for multi cable boxes.
Cable boxes have "MAC" addresses like a modem so they have to be setup. It would take me a long time to explain.