No. In the DocuSign pop-up window, you will see the Add Recipient button to include additional recipients, but their Sign Types are automatically set to "Send Copy". Quik! does not offer the ability to add signatures on the fly. The reason for this is there must be a signature field built into the original form in order for a recipient to eventually sign.
However, adding a recipient allows the user to include anyone to receive a copy, regardless of whether they have a defined role on the form. For example, if the user wants an assistant to receive a copy of the form and archive it, they can add him or her as an additional recipient.