Increase the max_user_connection value.
PHP Code:
show global variables like '%connections%';
Will help you in giving the no of connections you have set. Increase the number of connections. Max connections can be more than 16000 I guess, it all depends on your CPU, no of threads It can handle etc.
PHP Code:
SET GLOBAL max_user_connection=1000;
max_user_connections is a dynamic variable, which means you can directly run this query. You do not have to shutdown mysql.