Plesk daily job overwhelming MySQL

I am having an issue where the Plesk daily job (/usr/local/psa/admin/plib/DailyMaintainance/script.php) is overwhelming MySQL. This happens for between 5-10 minutes every day when the job is running. As far as I can see what is happening is that the job creates about 150-200 connections to MySQL and then other scripts are unable to connect. The max_connection limit for mysql is set to 512.

Is there a way to limit how many connections are used by the Plesk daily job?