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It can't hurt. I got a 3rd month CLI from $300 limit up to a $400 limit and now chat reps says I'll get a steps increase to $750 when before it was only going to be to $500.
Alright...I took it!
I always had the option to click "Request Credit Limit Increase" when you click "More" under "Services"
I didn't end up requesing one until my 2nd statement cut. However, some are granted a CLI before or after that, so YMMV. There's no harm in clicking it, just a lot of letters in your mailbox if you get declined.