Originally Posted by ddallas

You can earn as many points as dollars you can spend.

I believe the limits you are thinking about are when posters refer to not being able to earn the sign-up bonus points for the same card a second time.

They keep pretty good track of what promotional offers you have received in the past so if you apply for a card that is offering a 20,000 point bonus and you applied for that card previously and had received a 10,000 bonus, some posters are experiencing that amex only gives them 10000 of the current 20000 offer because they already received 10000 on a promo offer for that specific card. YMMV

If you have never had any of the cards before, and you applied for all of them and were approved for all of them, you would get all of the bonus points in the offers.