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function wpmudev_change_comment_settings() {
    global $wpdb;
​
    $blog_ids = wp_get_sites();
​
    foreach($blog_ids as $blog) {
            switch_to_blog($blog['blog_id']);
            $wpdb->query("UPDATE {$wpdb->prefix}options SET option_value = 1 WHERE option_name = 'comment_registration'");
            restore_current_blog();
    }
}
add_action('admin_init', 'wpmudev_change_comment_settings');