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There seems to be quite a bit of confusion about when CLIs are approved for BCE accounts in "credit steps." The Terms & Conditions clearly state that "Your credit line increase will go into effect by the end of the sixth month after your first payment." In other words, Amex can take up to eight months after the card was first approved to issue the CLI depending on when the first payment was made. The timing depends on when the first payment on the card was made, not the number of statement cuts.
Congrats on the auto increase! Did you try 3x CLI?