If your state has enacted the "Uniform Partnership Act" then it's a partnership, not a joint account. The law provides a statutory partnership agreement to govern the activity of those foolish enough to do business in this fashion.
The CIP regulation stipulates that your CIP address this situation if you allow it to happen:
(C) Additional verification for certain customers. The CIP must address situations where, based on the bank's risk assessment of a new account opened by a customer that is not an individual, the bank will obtain information about individuals with authority or control over such account, including signatories, in order to verify the customer's identity. This verification method applies only when the bank cannot verify the customerís true identity using the verification methods described in paragraphs (b)(2)(ii)(A) and (B) of this section.
Frankly, I would not allow it to happen; i.e. I would not open the account. (It sounds as if the folks who wrote your CIP dictated that result anyway.)
Four people who go into buisness together with so little forethought are likely to end up on the rocks somewhere.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.