Using Adobe Sign for Foreign Signed PDFs

I work for a local government and we Adobe Sign to send contracts through a lengthy approval process; User > Department Manager > Legal Dept > Finance Dept > Mayor > Clerk (for filing). This process works great when we are the writer of the contract.

The problem we have is when we aren't the one's who create the contract and we are receiving the contract from a vendor. In almost all cases, the vendor will be required to sign the agreement before the mayor can. So we receive an Acrobat certifed signed document. However, I cannot find a way to now send that document through our internal approval process. The only other option is to print it to PDF or Image and attached it into a new Adobe Sign request. 

Now the Clerk's office wants the signature panel on the orignal document to be included, but I cannot find a way to do that since the orginal docuemnt is not yet fully signed.