The reg says your CIP: "must describe when the bank will use documents, non-documentary methods, or a combination of both methods". So in some cases you may not even have one piece of ID.
The lead-in material to the CIP regulation clarified by saying at page 40: "a bank is encouraged to obtain more than one type of documentary verification to ensure that it has a reasonable belief that it knows the customer's true identity. Moreover, banks are encouraged to use a variety of methods to verify the identity of a customer, especially when the bank does not have ability to examine original documents ."