Pretty sure you can apply for all of them? You just have to do it in order.

If you're at 2/24 you can apply for THREE more Chase cards before you're cut off. Since you have 3 that you want, that's easy. After that you can get the Amex, albeit it will be much later.

Done.

5/24 means 5 cards or under, not under 5 cards so you're all set as long as the AMEX goes last!