AMEX T&C on all cards state you can't have had the card within the last 12 months. Most usually specify the family (Gold, Platinum, Zync). Usually no crossover biz to personal (i.e. you can get biz bonus when you have personal).
Sometimes they only disallow that card (i.e. if you have platinum you may still get gold).
How do you know what the terms are?
READ THE T&C ON THE APPLICATION PAGE. THEY ARE VERY CLEAR!!!Update 4/24/13:
It's no longer clear who
will get the bonus, but it's very clear who
will not receive it.
Beware of the new addition to the T&C of personal cards:
If you are identified as a current American Express® Cardmember, you may not be eligible for this welcome bonus offer.We don't know yet the effects, it can't be good, so take it into consideration. It might be a way to cut off churners even after a year of having the product.
You should always send a SM several times. There were multiple reports of success if persistent enough after being denied the bonus.
Don't bother calling, only SM! Don't give up so fast. Be creative and harsh. Say that a rep told you that you will get the bonus on the card. Follow up, demand an investigation and follow up again.
I am on the phone with a representative and she is saying that after May 1st, you are only eligible for bonus points on a card once in a lifetime for a card!
Please say this is not true