With the latest cPanel settings we can now assign the mail per hour limit for individual hosting account, so that no need to migrate the genuine clients on the new server for higher number of send E-mail limit.
Login in to the shell and open the respective hosting account user file.
cd: /var/cpanel/users/USER
and add the following line in the USER file.
MAX_EMAIL_PER_HOUR=400
We have assigned 400 E-mails per hours limit, you can set any limit as per your requirement.