This probably isn't going to be a possible solution that you want, but I cannot think of anyway in the Quiz settings that will allow multiple students to take the quiz together.
However the Assignment activity in the Assignment settings has Groups submission settings for students in groups a single submission. Now the quiz is not automatically scored like a quiz, but it does have advanced grading methods that make it easy to score. Unfortunately the assignment does not have a Response template function like the Essay question type which you could uses for those short question types.