For update requests, provide an option to not allow changes after the first response. If an update request is sent to multiple people, such as the primary recipient and a back-up recipient, once one of them submits a response, don't allow either recipient to change the response.
For example, a proposed visit date is sent to two people at a facility, the primary contact and her back-up. They are asked to respond on behalf of the facility as either 'Accept' or 'Reschedule' the visit date. Once one of them responds with 'Accept', don't allow either of them to change the response later.