It seems that the industry converged to the weird consensus where the digital signature of a file is stored in the file itself, on a crude imitation of paper documents. If I have a PDF document that must be signed by a bunch of people, I must sign the file, send the new version to another person, who will sign and create another file, which must be sent to the next person, who will create another file, and so on. This is obviously error prone and impractical, but this is how the only signing tool I have from my government allows me to do (I could also get a smartcard with direct access to the signing keys, but that is expensive and most people don't have it).
I want to do it in parallel: everybody gets the original unsigned PDF, sign it individually, send me the signed PDF, and I combine all the signatures into a single PDF file. Is this a supported workflow? Is there a tool to do that? Even if not supported and there is no tool, is that theoretically possible? Like, is there something in the PDF specification that would invalidate the signature if it is copied to another version of the document with the same contents, but more signatures?