If the message arrives in a single transmission, then Exim should removed duplicates in the process of delivery. This is unlikely to happen if the domains are different, or have been forwarded. Check your logs for the offending messages.
If the messages arrive in separate deliveries with the same Message-Id it is fairly easy to remove duplicates using that header. Exim will deliver using
procmail which can do the deduplication during delivery. During testing the duplicates can be delivered to a separate mailbox so nothing is lost.
I would encourage the user to unsubscribe from the duplicate addresses. A forward rule can be used to distribute to other addresses.