You won’t be approved for more than two Amex CREDIT credit cards in a 90 day period. Note, that charge cards are counted separately and don’t go into this 2 count tally. You can learn about the difference between charge cards and credit cards here.
I often have many of my clients apply for the Blue Business card and the Personal Gold card or Business Gold card the same day with success. Sometimes Amex will call the applicant to verify the second card to ensure that there is not a fraud situation.