Is there ever a need to have more than one W-9 to send to a customer requesting a copy?

Yes, a company may receive payments from one company where they are exempt from backup withholding and another company where they are not. For example, a corporation may be exempt from backup withholding in most cases but have a small division that received medical payments that are not exempt. In that case they may choose to claim exempt with most customers and send out a different W-9 that they do not check exempt for the medical services division.