Currently, an assignment can only be assigned to a single Group Set. The logic behind this is sound, as noted by Rob Ditto here: Allow assignments to be assigned to more than one group set.
My own current requirement, however is to be able to assign a single assignment to multiple group sets. Here's why: the course is a survey course which includes over 110 students. As such, there are 5 additional instructors in addition to the faculty member teaching the course who address smaller student groups. Each instructor has a group set which contains 7 groups, each filled with 3-4 members. The group sets and groups were created by the designer and not by students. They are self-signup, however, and all groups have members.
As we know that students do not belong to more than one group set, we would like to be able to assign the one assignment to each group set so that each of the 35 groups in the class is assigned the same assignment. There are other similar instances where, for instance, a class may be divided up into groups sets based on specialization: public health, disaster relief, disease prevention, etc. Really, anywhere you have a large group of students but still want to be able to develop group assignments could benefit from this feature.
I think the concern that Rob brings up about making sure that a student does not belong to multiple groups could be addressed by a rule similar to the one that prevents empty self-signup or manual groups from being used for group assignments.
I have inefficiently addressed my current need by replicating the assignment and assigned each replicated assignment to each group set.