You're not alone in looking for a solution for identifying contacts with multiple email addresses. I did some searching around and it appears others have asked a similar question in the community previously and they were directed to submit an idea. Looking through the replies, it seems this has been a request in the community for over 4 years now. I highly recommend upvoting this and sharing your use case for the functionality - the more noise we can make, the higher the chances HubSpot will add this into their product update roadmap. Upvote here!
One recommendation I did see shared is to implement a manual process, maybe monthly or quarterly, where you'd export all contacts and email address and filter in excel to identify those with multiple email addresses. It doesn't solve for the automatic notifications you're looking for but it's a start!
