Yup! I do it all the time! Go to www.disneygiftcard.com and you can set up an account and save and manage up to 5 cards. It is also good to register them in case they are lost or stolen. Disney has a chance of helping you.
You can merge multiple GCs onto a single GC with a maximum value of $1,000. You can have up to 5 GCs on record at any time but once you transfer the balance off of a GC, you can delete it and enter a new one.