Separate permissions for Portal and Email requests

Our organization has multiple Service Desk projects and would like to create unique permissions in the portal so that users can only see the service desk that applies to them. This helps to prevent the portal search from suggesting request options for the wrong service desk and misdirecting requests. However, we would like to keep allowing email requests from anyone, from any email address, with no restrictions. Currently the permissions for the portal and for email requests are combined. Can they be separated into two different permissions options? The current configuration is preventing us from using the portal in the way that it is intended to be used.