Apologies for this somewhat pedantic reply, but you may apply and receive a new Amex card with no hard check whatsoever. On the other hand, the new account will appear on your credit report once it is opened, so it will be no secret to other creditors that you have a new card.

In my understanding credit card users are too concerned with managing hard pulls. If your credit is good, adding a few hard credit checks to open your history will not make a material impact on your credit.