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As mentioned before why do you need a second amex? The best amex is going to be different for different people. It depends on your needs and whether or not you will utilize the benefits. I wouldn't even get a second amex unless you are really able to utilize it and it provides you with significant benefits. Amex has once in a lifetime bonuses, so its best not to apply for an amex card unless you really have a strong need/use for it and just hold out until there is the best bonus available for that particular product. There are some amex cards that don't do real bonuses like some of the business cards that give you 2 pts per dollar and it comes down to whether or not you are going to use the card.
Getting new credit cards should not be an end in itself.
Figure out what you want to do first. Is there somewhere you want to go? What airlines or hotel chains are most convenient for you? Do you want rewards that maximize your value on one airline or would you rather use a more flexible rewards scheme? What is your tolerance for annual fee? Do you care about status/lounge perks? How much are you willing to pay for them? Would you rather just get cash back? What categories get most of your spend? How many cards do you want to carry around with you?
Figure out what kind of rewards work best for what you want to do, then get the cards that will help you get there.