UI for using EDS when signing an agreement between legal entities?

Question

User interface

Given:
1. There is a service on which two legal entities can conclude an agreement
2. The agreement template generates a service, each of the parties can download it and sign it
Question: what should be the interface and procedure for exchanging the signed version of the document in this case? As well as verifying that the document is signed by both parties. Each of the parties must see that the document is signed by him and / or the other party. When you click on the control document, it is transferred to some conditional plugin of the conditional Crypto.Pro. What happens to the document after signing? How does the document get to the server after signing?