by Brian Crow:
Your original deposit contract is with two people, it takes two people to modify the deposit contract. If the party wanting to add a new owner doesn't want to seek the approval of the other joint owner, kindly request that they open a joint account with just themselves and the person they are wishing to add.
by John Burnett:
The answer could be different if the request is to add an attorney-in-fact or agent (AIF) for one of the two joint owners. Unless the deposit contract prohibits it, adding one owner's AIF as an authorized signer is probably not something you can refuse to do. In such a case, I recommend promptly notifying the other joint owner to give him or her the opportunity to sever the joint account relationship if he/she objects to having the AIF added.