As most WordPress projects are barely designed to have a huge amoung of users, this is not necessary in most cases. Anyway, the following code will help with this problem – add this to your functions.php-file and the WordPress user search will scan first name, last name and e-mail of every user.

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   // the actual improvement of the query
    function user_search_by_multiple_parameters($wp_user_query) {
        if(false === strpos($wp_user_query -> query_where, '@') && !empty($_GET["s"])) {

            global $wpdb;

            $uids=array();

			// get the custom meta fields to search
			$iusib_custom_meta = get_option('iusib_meta_fields');
			$iusib_cma = array_map('trim', explode(",",$iusib_custom_meta));

			$iusib_add = "";
			// the escaped query string
			$qstr = mysql_real_escape_string($_GET["s"]);
			
			// add all custom fields into the query
			if(!empty($iusib_cma)) {
				$iusib_add = " OR meta_key='".implode("' OR meta_key='",$iusib_cma)."'";
			}

            $usermeta_affected_ids = $wpdb -> get_results("SELECT DISTINCT user_id FROM ".$wpdb->base_prefix."usermeta WHERE (meta_key='first_name' OR meta_key='last_name'".$iusib_add.") AND LOWER(meta_value) LIKE '%".$qstr."%'");

            foreach($usermeta_affected_ids as $maf) {
                array_push($uids,$maf->user_id);
            }

            $users_affected_ids = $wpdb -> get_results("SELECT DISTINCT ID FROM ".$wpdb->base_prefix."users WHERE LOWER(user_nicename) LIKE '%".$qstr."%' OR LOWER(user_email) LIKE '%".$qstr."%'");

            foreach($users_affected_ids as $maf) {
                if(!in_array($maf->ID,$uids)) {
                    array_push($uids,$maf->ID);
                }
            }
			
            $id_string = implode(",",$uids);

            $wp_user_query -> query_where = str_replace("user_nicename LIKE '%".$qstr."%'", "ID IN(".$id_string.")", $wp_user_query -> query_where);
        }
        return $wp_user_query;
    }