$meta_query = array('relation' => 'AND' /* and other base meta query settings */);
$sub_query = array('relation' => 'OR');
foreach ($colors as $color) {
$sub_query[] = array(
'key' => 'project_color',
'value' => '"'.$color.'"',
'compare' => 'LIKE'
}
}
$meta_query[] = $sub_query;