For a long time it has been possible to open an American Express authorized user without entering a SSN. In the past this was much more useful for small business Saturday and AmEx offers. In fact it wasn’t unusual for churners to add up to 99 authorized users to take advantage of this.
Last year we saw American Express close some inactive authorized user accounts and anecdotally American Express has been allowing authorized user accounts to be opened with no SSN closing these accounts if a SSN wasn’t added within 60 days.
It seems like this is no longer possible (and might not have been possible for the last month or two) and American Express is requiring the SSN at sign up. ITIN’s continue to work in place of SSN.

