To limit My Portal cases per brand, record which brand each case is regarding as a case custom field. Then, within "My Cases (List)" you'd use this code.

gistfile1.html

<table class='mycases'>
  <thead>
    <tr>
      <th></th>
      <th>{{desk.system.snippets.case_id}}</th>
      <th>{{desk.system.snippets.subject}}</th>
      <th>{{desk.system.snippets.from}}</th>
      <th>{{desk.system.snippets.created}}</th>
      <th>{{desk.system.snippets.status}}</th>
    </tr>
  </thead>
  <tbody>
    {% for case in desk.page.content.cases %}
      {% if desk.current_brand.name contains case.custom_brand %}
        <tr>
          <td class='a-casechannel'><img src='{{ case.channel_icon }}'/></td>
          <td class='a-caseid'>{{ case.id }}</td>
          <td class='a-casesubject'><a href="{{ case.portal_url }}">{{ case.subject }}</a></td>
          <td class='a-casefrom'>{{case.customer.first_name}}</td>
          <td class='a-casecreated'>{{ case.created_at | in_time_zone: site.timezone | date: '%b %d' }}</td>
          <td class='a-casestatus'>{{ case.status.name }}</td>
        </tr>
      {% endif %}
    {% endfor %}
  </tbody>
</table>