Answer:
Only if your bank allows it... One of my partners is fond of saying, "Customers don't open accounts, banks do." You are entitled to say what the requirements are.
The age of the second party is not the primary issue here. It is that fact that she is not present and someone wants to you to enter into a contract using her name. Bad idea.
When the 16 and the 19 year old are in your institution wanting to open a joint account, then it is appropriate to see if her age is an issue under the laws of your state and your institution's policy on dealing with minors.
First published on BankersOnline.com 5/20/02