Try using tax_query:

$tax_query = array(
    \'relation\' => \'AND\',
    array(
        \'taxonomy\' => \'category\',
        \'field\' => \'id\',
        \'terms\' => 1
    ),
    array(
        \'taxonomy\' => \'category\',
        \'field\' => \'id\',
        \'terms\' => 2
    ),
    array(
        \'taxonomy\' => \'category\',
        \'field\' => \'id\',
        \'terms\' => 3
    )
);
$query->set( \'tax_query\', $tax_query );