I'm not sure I understand the question. But for tasks, you have an assignment group. That is the group that is responsible for resolving the task. Then on e.g. CI's you can have a field Support group. That is just to know who does the support on this CI. In other words, if there is an incident on this CI, put this group as assignment group. This is one of the reason customers have functionality that when you fills in a CI on an incident, it takes the value of that CI's Support group and put that in the assignment group on the incident (task).

This is my thoughts and I hope this made it a bit clearer.