add an Alternative counter-signer after the webform is sent out

Hi! I am just starting to use the webform and our process is like below:

created a webform and its url posted on a website => one of the client open and fill it up to request information from a department ==the webform then needs the signature from the authorized person of the department (dynamic field to be check against the database) ==> webform routed to the the authorized person of the department for signature => completed

The webform has been created that the whoever requests has the role of Approver, the process control person(IT) has a role of counter-signer. We could add the authorized person of the department to the counter-signer group and it worked as expected. We are moving forward to auomtate the entire process but couldn't find any REST API model schema that would allow such update during the process. We would like your help on this issue, thank you!