If it is the same node ID that gets shown several times, this will do it:

function example_entity_view_mode_alter(&$view_mode, $entity) {
  if ($view_mode !== 'teaser' || !isset($entity) || $entity->getEntityTypeId() !== 'node' || $entity->bundle() !== 'partner_program') {
    // This would not be our view, bail early.
    return;
  }
  static $nid;
  if (isset($nid) && $nid === $entity->id()) {
    // This partner program teaser has already been displayed on this page,
    // display this additional sequential partner program without an address.
    $view_mode = 'teaser_without_address';
  }
  else {
    $nid = $entity->id();
  }
}

But that’s not actually my situation or a common one. The need is probably more likely to be like this:

function nchfa_custom_entity_view_mode_alter(&$view_mode, $entity) {
  if ($view_mode !== 'teaser' || !isset($entity) || $entity->getEntityTypeId() !== 'node' || $entity->bundle() !== 'partner_program') {
    // This would not be our view, bail early.
    return;
  }
  static $partner_id;
  if (isset($partner_id) && $partner_id === $entity->field_partner_id->value) {
    // This partner program teaser has already been displayed on this page,
    // display this additional sequential partner program without an address.
    $view_mode = 'teaser_without_address';
  }
  else {
    $partner_id = $entity->field_partner_id->value;
  }
}