Like virtually any creditor, they will almost never say "no" when they get a chance for more income, such as issuing multiple cards on one account. Depending on the card, there will be additional fees. If it is one of their charge accounts, like the Gold, Plat., or Centurion, you will pay an additional yearly membership fee per card. You also get significantly more points with each additional card. The card itself will have your name on it IIRC.
As others have said, I too, have read that AMEX is not good for building credit (if that is what you are trying to do). IIRC they do not report to all three credit bureaus, where as many other cards do. Orchard Bank is often good for building credit. However, their cards usually have a yearly fee.