There is not a way to prevent additional addresses from being added to the integrated record.

For example, the student record in Education Edge and the Constituent record in Raiser's Edge have the same address, which is linked in Match details, but there is also an additional address on the Constituent record that is marked to be added to the shared record. (not mapped up with an existing address). This cannot be removed.

Once the addresses are added, they can be manually deleted from the record.