A twenty foot container will easily hold two cars inside. Generally when cars are shipped inside a twenty foot container, they are shipped two at a time. Both cars are placed on the floor of the container. There is no additional room to add cars above them.
For the creative shipper a forty foot container can hold as many as four cars inside. Two cars are placed on the floor of the container and the other two are suspended above them. It is important that the shipper use a heavy duty steel wire or chain to suspend the cars to prevent it from failing and the cars becoming damaged. When done correctly, all four cars are transported without any movement or damage.
However, some shippers pride themselves on only shipping three cars per forty foot container. They will place two cars on the floor of the container and suspend only one above them. This often appeals to customers because it seems less packed than the traditional four cars.
Regardless, you can often make requests to have as few cars as you would like shipped in the container with your car. You can insist that no cars be above yours or even to the side. It will cost you additional money to have your car shipped alone, but it can be accomplished.