We have group assignments, how about group quizzes?
Problem: Students meet together to take a quiz as a group activity. Currently, one student (or more) will be the "sacrificial lamb" and will take the quiz and learn which answers are incorrect. Sometimes a second student will then take the quiz and see if they can get the correct answers. Eventually, they find all of the correct answers so then the group leader takes the quiz and gets a 100%. This is not the way we want them to 'learn' and the point is not to get 100%, but for them to work together and for the teacher to find where the holes are in student learning.
If we could set up the assignment to be a group quiz, then students could only work through it once because only one submission could be made by the group (if we put that in the setting criteria).
