If you need to get the exact same document signed by multiple users which results into multiple signed documents with one signature you can use the bulk send feature.
The recipients will not see the details of other recipients while using the "Bulk send" feature.
First, you'll need to create a template (only option 1 works for the bulk send) within SignRequest. After creating the document you can select "Bulk send" on the template page.
The following video shows you the necessary steps.
With the bulk send feature you can send a SignRequest to up to 1000 signers at once. Please make sure to test the template extensively with several of your own email addresses before sending out a bulk send.
Note, that if you add multiple recipients in the normal SignRequest "Contact(s)" field they will all sign the exact same document, see each other's details and all signatures will be added to one contract. (Thus, for example 10 signatures on one document, instead of 10 documents with 1 signature which is the case with the bulk send feature.)