Element Criteria Model: filtering by empty values
Okay, doesn't seem to be the most elegant but the only way I could achieve this was by carrying out the entries criteria query within my $fields loop. So, for example:

$entries = [];

foreach ($fields AS $field) {
    $criteria = craft()-&gt;elements-&gt;getCriteria(ElementType::Entry);
    $criteria-&gt;limit = NULL;
    $criteria-&gt;$field = ':notempty:';
    $tmpEntries = $criteria-&gt;find();

    $entries = array_merge($entries,$tmpEntries);
}