multiple itunes accounts one computer

We have 3 separate I-tunes accounts in our house. I want to store all the music on one computer. When I try to download recent purchases from Account A, it says that the computer is an authorized device (although it doesn't show up under devices), but then tells me that if I download recent purchases from Account A today, I can't download any previous purchases from any other devices for 30 days.

Does this mean I can only backup our purchases on a single computer once every three months?!