Yes, credit cards that are co-branded with major credit card associations (MasterCard, Visa, etc) are subject to BO.
Page 80 of the Final Rule:
In contrast, credit cards that are co-branded with major credit card associations do not possess the same limitations and characteristics that would protect them from abuse. For example, co-branded credit cards can be used at any outlet or ATM that accepts those associations’ cards. FinCEN therefore believes that covered financial institutions should obtain and verify beneficial ownership information with respect to opening accounts for legal entities involving such co-branded cards.
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CAMS