Earlier quoted context omitted.
You could do some scheme that hashes a site specific identifier with an identifier on the smart element of the id. If that ever repeats, the same I'd was used twice. At the same time, the site ID would act as salt to prevent simple matching between services.
People do, in fact, have multiple profiles. For very valid reasons.
If you need to verify even more accounts the government can have some annoying process for you to request another batch of IDs.