Avoid Save As dialog when Signing a document in Acrobat?

I'm working on a web application that allows users to download a PDF, sign it, and then upload it back to the server. I'm trying to minimize the number of steps required of the user, so I would like to by-pass the Save As dialog that is presented when a user signs a document in Acrobat.  Is there a way to do this?

Basically, I would like the signed document to be saved *automatically* in one of the following ways:

1. Automatically overwrite the original document

2. Save to the same location as the original document, but with a different name (e.g., [original_name]_Signed.pdf)

3. Save to a subdirectory of the original document's location (e.g., in a "Signed" folder)

Is this possible using JavaScript or a custom plug-in? Or in a simpler way?