Unfortunately the bbs only offers two options, keep or delete.
After deleting the ones that you don't want to keep, and you still haven't enough room, you may have to create your own archive file and copy/paste individually the ones you want kept before deleting them from your PM inbox to make room. Most users experience the full inbox syndrome at around 2000 PM's.
Edit Note; My apologies, I stand corrected, the number is 500 for received messages.