You should be able do that by adding the 'moodle/local:assignuserposition' capability to the 'manager' role.

Each manager is given the manager role in their staff's user context, so that should only give them permission to modify their staff's details (unless you've assigned the manager role to someone in the system or other higher context).

One small issue - if a manager changes one of their staff's manager to someone else, they will lose the ability to edit so they won't be able to switch it back themselves.

Simon