I doubt this will work for you as I'm sure your drives are different makes and models- but if they were identical you could get the 4 external drives to auto-mount using the same password as each other. I don't believe you can have the FDE password unlock your external drives, so the best case scenario would be to enter the password twice (FDE, and once again for all the external drives).
We had the same problem a few months ago and solved it completely by accident.
One of our external backup drives failed, so we replaced them all with the same model (WD Elements 1TB).
As soon as we started using the same model drive, we stopped getting prompted for the second drive- it authenticates using the password from the first (until TrueCrypt or the server restarts). Now, when I update the server and do a reboot at the weekend, I can remote in, and enter the TrueCrypt password for whichever backup drive happens to be connected. Then, when the staff switch the backup drives over later on, the password prompt does not appear again with other drives (as it used to do).
There is no loss of security, just a big improvement in convenience and reliability of our backup system now- all it seems to need is identical model external drives.
I am reasonably confident that this is the best solution to your problem. I wrestled with this for hours when we first started using TrueCrypt on multiple drives, and initially admitted defeat. The fact it does what we want now is due to the fact the drives are identical, rather than some setting I could use in the application to produce the desired behaviour.
No one in the office could believe that the solution didn't lie in the TrueCrypt configuration settings!