It is not possible to assign one issue to more than one user at the same time. The most common suggestion is to create one sub-task for each person.
However, if you don't like to do this, you can also create a custom-field of the type multiple-user-picker and show it on the sub-task screen. All users can now search for issues where they are part of this field.
Please not that a custom-field will not work like the system-field "Assignee" for reports as e.g. User-Workload or filters e.g. "Assigned to me" and other such things.
JIRA doesn't allow this feature directly to avoid overloading. However, you can do this. Refer this doc.
I would prefer the second option to manage via a group (multi picker custom field). You can give permissions to that group as similar as Assignee
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