How to let multiple people digitally sign a document after the document is locked?

So there is one document where I let the other party sign first, but the signature of the other party locked the document, which blocks me from signing. How do I circumvent this without asking the other party to not lock the document after their signature?

For example, I saw this article https://support.globalsign.com/aatl-document/multiple-signatures-adobe-acrobat-xi where you create pre assigned fields for digital signatures. If I created these fields, and let the other party sign first, would I be able to still sign the document even after the document has been locked?

Thanks in advance.