Looking at the templates in the projects section, specifically the new business unit ones

Is it possible to set task assignment to a group, rather than a specific agent? For example; we want to copy the new employee project template and modify it to employee moves/transfers.

One task in that will be to move the employee off distribution lists that are no longer relevant, and onto ones that are. Can we assign that to our Service Desk group so it is visible to ALL agents in the group?