If the signers don't trust the other signers in the same non-profit, then maybe they shouldn't be associated with that non-profit.
Regulation P allows you to share information in order to service an account which you are doing. Also Regulation P applies to consumer accounts, not information collected in conjunction with a non-profit. (See 1016.1(b))
(b) Scope. (1) This part applies only to nonpublic personal information about individuals who obtain financial products or services primarily for personal, family, or household purposes from the institutions listed below. This part does not apply to information about companies or about individuals who obtain financial products or services for business, commercial, or agricultural purposes.
Any accomodation you make to provide seperate documents to obtain account signer information is a business decision.
I would also add that signers on a business account are not considered customers according to the USA PATRIOT Act so unless your board approved CIP requires it, you do not have to obtain social security numbers from business account signers. (Of course, the beneficial ownership certification is another story, but you'd only need a control prong for a non-profit.)
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