Can't add a new seller to Adobe Digital Editions because my computer is already authorized

I recently bought some epub books from Books-a-Million. In order to read them I have to use Adobe Digital Editions, which means I have to add Books-a-Million as a seller to Adobe Digital Editions and put in the password of my Books-a-Million account.

Books-a-Million says I need to click on "Authorize Computer" and then click on "Ebook Vendor" to add my Books-a-Million password. But Adobe Digital Editions won't let me click on "Authorize Computer"; it's greyed out because my computer is already authorized with my Adobe ID. I could presumably de-authorize it, but then I'd lose access to content I already own.

So how do I add a new Ebook Vendor without deauthorizing my Adobe ID?