Realize this is an old question but still unclear whether or not an ITIN is acceptable for CIP. Can a bank decide to accept it, if additional ID verification is complete (i.e. Valid DL, passport etc.)? Under CIP rules opening account without a SSN or TIN is not permitted. So if a new account is opened with just an ITIN is that a violation? We do have some accounts with ITIN's only and BSA examiners get a list of those when we're examined but have never been sited with a violation.
The regs say that you need a US Identifying number for a US person. For a Non US person, it could be an ITIN, a passport or an alien ID card. But your bank has to state in their policy what they will accept for the two groups: US person and Non US person.