When you download ADE to a computer, you authorize it for that computer through an Adobe ID that you set up for your account. But it isn't the copy that is authorized, it is the Adobe user ID it is authorized to, so you can change users but unauthorizing and re-authorizing with a different Adobe ID and the maximum 6 devices are synced to the Adobe ID, not to the copy of Adobe Digital Editions.
So when ADE is first downloaded, it is authorized to whomever downloaded it.
Again, once ADE is downloaded, it isn't technically that copy that is tied to that computer, but that authorization Adobe ID. So with Adobe Digital Editions open, you can deauthorize it and then re-authorize it as a different user. The Command CTRL-SHIFT-D while in ADE lets you deauthorize it.
When you click the Library dropdown in ADE and select "Authorize user"
Then you can authorize that copy as a different user.
Note that if you plug a device you have authorized to your copy of ADE into a copy of ADE that is authorized with another Adobe ID, it will not recognize your device unless you unauthorize and reauthorize with your Adobe ID. In short, eReader devices themselves are tied to an authorization once they are used with ADE, So once I have used a device in ADE authorized with my Adobe ID, ADE authorized with other ID's will recognize it.
So if you can't get a copy of ADE to recognize your device:
eReader devices themselves are tied to an authorization once they are used with ADE, So once I have used a device in ADE authorized with my Adobe ID, no other ID's will recognize it.