It is possible as long as you have the global "Bulk Change" permission.
see: https://confluence.atlassian.com/display/JIRA/Managing+Global+Permissions
If you have that permission see https://confluence.atlassian.com/display/JIRA/Using+the+Issue+Navigator#UsingtheIssueNavigator-Workingwithissues
When performing bulk changes, the assignee is changed.. sometimes it seems to change based on the component lead. Is there a way to disable the assignee being changed?
What kind of bulk change are you doing (edit, transition,move)?
Move
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