Give something like this a try: (it came from the same page you linked to, just scroll down a bit more).
$args = array(
'post_type' => 'post',
'tax_query' => array(
'relation' => 'AND', // searches for posts meeting both conditions
array(
'taxonomy' => 'midgets',
'field' => 'slug',
'terms' => array( 'tagA,TagB' ), // searches for EITHER tag
),
array(
'taxonomy' => 'donkeys',
'field' => 'slug',
'terms' => array( 'tagX,TagY' ), // searches for EITHER tag
),
),
);
$query = new WP_Query( $args );