Due to the impossibility of verifying a name/TIN combination in this circumstance, you will likely develop a watered down version of your CIP, a "BOIP," where you indicate you will "verify" nothing more than name, address, and DOB from a photocopy of the individual's identification. (As noted, the CIP regulation never required banks to verify all four identifiers, just enough to form a reasonable belief of the person's identity.)
If it sounds like a waste of time, you understand...
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.