Improved assignee searching - multiple assignees

We have just transferred our issue tracking system to Jira, and because it is project based, hundreds of issues that got lost because they were unassigned have appeared. However I now cannot distinguish between issues that were previously lost and need to be dealt with, issues that are assigned to me or my team and need to be dealt with, and issues that are assigned to other departments and can be ignored.

We have a team user account for our team. Ideally we should be having a group, but our Jira admins paid no attention to our processes when setting the Jira system up. Nevertheless, even in the long term it would be useful to be able to filter on issues where the assignee is:

Unassigned OR me OR team mate 1 OR team mate 2 OR ... OR team account

Even if we get a Jira user group set up for our team, it would still be nice to be able to search by Assignee = Unassigned OR team's user group.

I imagine it would also be useful to some people to be able to search for faults assigned to users in one or more of multiple user groups.