It doesn't ever work in my experience - as soon as you do it, you lose issues to "I though the other guy had it", so Atlassian's firm "you are the assignee, it is your responsibility" is a delight to those of us who've worked with task allocation systems for any lenght of time.
There are a number of ways you can make JIRA represent some form of group ownership (some are botches IMHO, but if you're determined to get it wrong, they're valid ones), but the assignee still remains, rightly, a single person. See https://confluence.atlassian.com/jira/how-do-i-assign-issues-to-multiple-users-207489749.html
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