It's not possible to assign an JIRA issue to multiple assignees.
You can have only one assignee per JIRA issue. An work-around for this problem can be to add related people as watcher. Or you can use a custom field of type "Multi user" user picker wherein you can select multiple users.
Or use sub-tasks as intended - break down the work into bits and assign the parts out.
Or use a group picker to indicate a group responsible.
But, always have a single person "own" the main issue by being assigned it. In real life, multiple assignees only works in two narrow conditions, and in neither of them do you actually need it.
I agree with @Nic Brough [Adaptavist]. Managers want to know who is responsible and ultimately it has to be one person; the Assignee. The assignee needs to manage anyone else working on the issue. they could create subtasks to the main issue and assign them to who is responsible for that part.
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