In Asana, the work-management software from San Francisco, a task can have only one assignee. The company explains why: “Having only one assignee per task ensures that there’s never a sense of ‘who’s responsible for completing this task?'”
It describes what happens otherwise: “Let’s say there were two assignees on a task, one person may think the other has the ball, and vice versa.” Other people can follow the task and be kept informed. Only one person owns it.