At the root of the core Moodle is the school or institution, the client in your case. One can partly simulate multiple institutions by giving a course category to each. But it does not provide a clean isolation. The Moodle Workplace Mary mentioned is a recent product from the makers of Moodle. The other alternative is a derivative of Moodle called iomad, from an active Moodler here.
You will find more about this topic if your search for multi-tenancy in the forums. For example multi-tenant LMS or Applying Moodle on a large University in the General help forum.
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