In general, most server control panels provide functionality to limit the number of outgoing messages. In this post, I’ll show you the ways to limit outgoing messages in the Plesk control panel. Please take note that this functionality is only supported on the Plesk version 12.0 and above.
Launch your web browser and sign in to your Plesk account as you normally would. Click on Tools & Settings link under the Server Management on the left.
Then click on the Mail Server Settings under Mail. Scroll down and check the option Switch on Limitations on outgoing email messages. Uncheck the unlimited check boxes for Default Limit on outgoing messages from a domain (per hour) / subscription (per hour) and enter the limit for the number of messages can send per hour. Click on OK button at the bottom to apply the changes.