Hi @ E J ，
Yes, based on my research, built-in notifications for outbound spam can be global admins or designated recipients. However, similar notifications cannot yet be sent to spammers.
For more information, please refer to this link: Outbound spam protection - Office 365 | Microsoft Learn
For users who need to send bulk mail, please refer to the recommended solutions in the official article: Recommendations for customers who want to send mass mailings through EOP - Office 365 | Microsoft Learn
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