Your requirements for identification are dictated by the terms of your CIP. Make certain that it covers this scenario. If it does not, make certain that one of your predecessors did not omit the option on purpose. A decision could have been made not to open accounts for non U.S. persons and the simplest way to communicate that would be to leave it out of the CIP.
If you do open the account, you should be able to identify them as "non U.S. persons" if you are asked for a list of this category of customer in an expanded BSA examination.
I suggest that you do not open an interest bearing account for these or any other non U.S. persons. As Magic City notes, that would trigger a W-8 requirement and it would also trigger information reporting on a form 1042S. You would have to know as much about IRS compliance to bank one foreign customer as you would if you banked 100 foreign customers...
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.