If the database files are of the same database, with the same serial number: 

Only attach one database at a time.

If the database files of databases in which the serial number of the original has been changed: 

1. Log in to the original database and verify that the serial number has been changed
2. Open the Blackbaud Management Console (Blackbaud Management Console) and detach the original database
3. Attach the duplicate database
4. Attach the original database