Whether we can solve unblock outgoing email by myself? or Whether we can add the quantity of daily mail bounce count exceeds limit?

Whether we can solve unblock outgoing email by myself? or Whether we can add the quantity of daily mail bounce count exceeds limit?

Details :Mail Outgoing blocked.

Reason :Daily Mail Bounce Count Exceeds Limit [ Bounce count=11 ]  

Our company always  need to send email about new product or promotion to all our customers,  which title is similiar and is always blocked. Both of us always need more time to solve this problem.  Whether there is any good idea to solve this problem? Whether we can solve the problem that mail outgoing blocked by ourselves? Or whether we can add the quantity of daily mail bounce count exceeds limit? 

Thank you!