A grantor trust is a formal trust agreement under which the grantor/trustor retains the right to rescind or cancel the trust and recapture assets placed in the trust. Typically, although I imagine there are exceptions, the grantor is the trustee of such a trust.
If the trusts you are looking at meet the IRS's requirements for a grantor trust that can be ignored for reporting purposes (so it uses the grantor's TIN instead of getting its own), you can accept such a trust. The trust would be your customer under CIP rules, and I don't see a CIP problem.
To avoid name/TIN mismatch problems if the account earns reportable interest, you'd probably consider setting them up with the grantor's name as part of the account title.
If you have any concerns about whether the trusts meet the grantor trust definition, you should ask bank legal counsel.
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John S. Burnett
BankersOnline.com
Fighting for Compliance since 1976
Bankers' Threads User #8