Hello,
Thank you for contacting us about changing the max_connections on a dedicated server. You will need to edit the MySQL my.cnf to increase the max_connections.
However, often this may not address the cause of issue, since typically this is caused by a coding issue. For example, it should open, then close the connection. Instead of leaving them open for long periods of time.
If you have any further questions, feel free to post them below.
Thank you,
John-Paul B