global $odb;
$db_user = "Your DB Username";
$db_pass = "Your DB Password";
$db_name = "Your DB Name";
$db_host = "Your DB Hostname";
$odb = connect_to_intermediary_db( $db_user, $db_pass, $db_name, $db_host );

function connect_to_intermediary_db( $db_user, $db_pass, $db_name, $db_host ) {
    $db = new wpdb( $db_user, $db_pass, $db_name, $db_host );
    return $db;
}

/*
 * You can now use $odb the same as you would
 * $wpdb, but it is connected to your custom
 * database.
 */