Laravel 5.1: PDOException: has exceeded the 'max_user_connections' resource

I am running functional tests in Laravel 5.1 against a MySQL Database on a staging server and get the following error:

PDOException: SQLSTATE[HY000] [1226] User 'username' has exceeded the 'max_user_connections' resource (current value: 20)

Is there anything beside raising max_user_connections I can do to control how much parallel db connections are open? If possible I do not want to slow down the tests :)

On my local dev machine max_user_connections is set to 0 so there is no limitation and no error.