I don't think that's currently possible. The way the system works currently is that all required parties need to sign the document before the deadline. If you upload a document that has already been processed by the system (e.g. all parties signed before the deadline and the PDF with sigs was generated), it won't be accepted since it is encrypted.
It sounds like you are looking for a workflow component with multi-level signatures. That isn't currently part of the eSignatures service, but Adobe does offer server products (LiveCycle, on which the eSignature service is based) that can do this. Maybe in the future.