Personally, I've always taught tellers and New Account Reps, if something seems unusual, it probably is - If the bank is uncomfortable with a request made by a customer, they are under no obligation to heed that request - simply tell the customer, that in this situation you are uncomfortable with the inordinately large number of signers on the account and will not allow it.
(Out of curiousity, how many is she asking for? 3, 9, 12?)
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My comments are absolutely no reflection of, nor influenced by, my employer - take them at your own risk.