I need to change the Case Manager for a group of people

You can do this by running a Search from each of your Search screens for the old Case Manager:

From the Case Record Results, choose Action, Change Case Manager

Select the new Case Manager from the drop-down along with an Assignment Date:
Save
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Everyone included in the search should now be assigned to the new Case Manager. You can do this for Mentees, Mentors, and Matches.