Hi Amanda ,
You can group a users in one role and then set "manage users " permission.
Manage users is a global permission, so all users that belongs to a given role and that have this permission set will be able to change details of other users as well.
Another option is crating a simple user or custom control that uses the api and your users can update all details using this widget. You can drop the widget on a backend or frontend page depending on you will grant your users with backend access or not.
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