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If the Amex CLI is more important to you than the GE one, then you should rationally hold off on calling GE. Prioritize your goals and chase them in order as I do think a GE-CLI might affect your Amex chances. Amex wants your transactions first and foremost, so if you're trying to build limits through CLI's there (which are worth more in my estimation than any GE-backed card) I don't think it'd help, and it might hurt, to be asking for more credit from other lenders... especially as Amex wants to see a stable credit file and their CLI granting appears to not track with their consumers other limits.