Adding Additional Signatures

Yes, it is possible. You create the envelope dynamically only after the user submit the form. At that point you know how many signers and all the information you need I assume. So you create the envelope with that in mind. https://developers.docusign.com/docs/esign-rest-api/how-to/request-signature-in-app-embedded should help. Simple C# code (add singer2 etc. for your use case):

Signer signer1 = new Signer {
        Email = signerEmail,
        Name = signerName,
        ClientUserId = signerClientId,
        RecipientId = "1"
    };
   
    // Create signHere fields (also known as tabs) on the documents,
    // We're using anchor (autoPlace) positioning
    //
    // The DocuSign platform seaches throughout your envelope's
    // documents for matching anchor strings.
    SignHere signHere1 = new SignHere
    {
        AnchorString = "/sn1/",
        AnchorUnits = "pixels",
        AnchorXOffset = "10",
        AnchorYOffset = "20"
    };