They generally require the SSN for the add'l person and run a credit check on him/her. If you don't happen to have the number with you, they WILL issue the card for the other individual and YOU will be exclusively responsible for any charges posted to that new account (last 5 digits will be different). You will need to activate the new card once it's sent out, since they will send it only to your address under these circumstances, and will typically ask for your birthday, the last 4 digits of your SSN, etc.