Adding a OpenPGP signature to an already signed document?

We'd like to implement a workflow that requires multiple people to digitallly sign a document. If I have multiple secret keys in my own keychain, I can do something as simple as:

gpg --sign -u userid1 -u userid2 filename

But what do I do if I've got an already signed document and I want to add a signature? One solution would be to have everyone generate detached signatures for the document, and then package them all together in a zip file or something, but the overhead there is substantially higher. Is there a better way?