Usually, all members of the team have their own doubling cube vs. the box, and can double regardless of what other team-mates do, and they can accept or refuse a double independently of the other players. The result is that, although they are using a single backgammon set, each member on the team is playing a separate game against the box.
In most cases, team members have their own doubling cubes in relation to the box, enabling each player to decide whether or not to double on their own terms. As a result, despite sharing a single backgammon set, each member plays a distinct game against the box.