Hi, what you need to use is a Powerform. Poweforms are template-based and don’t require the sender of the document aka YOU, to provide the recipient details. When setting up a Powerform, you get a link that you can share via email or embed on a website.

Whoever clicks on that link will be able to provide the name and email of the signers.

I’ve created a video about they work and how you can them one up here: 

Let me know if you have more questions!

Sofian Saoudi,
Solusign Consulting DocuSign Partner

Need help with DocuSign?

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A feature that might help is called Signing Groups.  It works best for internal workflows where the group will be used frequently.  It could be used for external groups too however the setup of a group that is only used once may feel a bit cumbersome. 

There is also the ability for recipients to change signing responsibility if they determine another is the appropriate signer, however this would not notify all possible recipients at the same time as you mentioned.

Another option is to look at the role of Specify Recipients.  As most of the clients I work with have this and as you are already in conversation with the company send the documents to your contact with that signing type and then they can enter the name and email of the signer.  Also as @MPelham suggested Signing groups is another option where you send to the group and one of them can sign does not matter who signs.