Does anyone allow a customer opening an account to have the person they have moved in with (such as a family member), sign a note saying they live with them at their address when the customer's ID doesn't match the new address and they say they don't have any utility bill or any document with the new address?

I would refer to your BSA/CIP policy to identify what steps/documents are required in such instances. If your policy says that if the address provided by the individual does not match the address on the photo ID that you are required to obtain specific types of documents to verify they address they provided, then based on your policy, you cannot open the account. However, if you use an automated identity verification application, it may confirm that the address on the ID is a valid address for the individual. Your policy may allow the account to be opened in such instances with a specified timeframe for the individual to provide documentary evidence of the address before the account is closed. It all depends on what your policy states and what verification is required. As noted in the FFIEC BSA/AML manual, "The CIP must contain risk-based procedures for verifying the identity of the customer within a reasonable period of time after the account is opened. The verification procedures must use the “information obtained in accordance with [31 CFR 1020.220(a)(2)(i)],” namely the identifying information obtained by the bank. A bank need not establish the accuracy of every element of identifying information obtained, but it must verify enough information to form a reasonable belief that it knows the true identity of the customer. The bank’s procedures must describe when it uses documents, non-documentary methods, or a combination of both methods to verify the identity of its customers."