If this individual is becoming a joint owner of an existing account, the CIP
Q&A document indicates that a new customer relationship is being established (see question #2 under the heading for "Definition of Customer" on page 4). That would require that you obtain all four of the identification elements required by CIP, and that includes the SSN.
If the individual is being added as an authorized signer (not a co-owner) on an existing account, the CIP regulation doesn't consider the individual a customer from whom you must obtain ID information. However, if your bank's CIP requires that you "CIP" such individuals, you must, or your bank can be cited for not complying with its own policy.