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I've had the Chase IHG card since 2013. My SL was 3500 and it's still 3500.
I have pretty good credit (726-760s) and they wont give me a CLI with their 4k limit. I like the card and enjoy spending on it but $4k is pittens. I'm going to downgrade it for Amazon only duty and that's basically it for the 5% back.
I think I've had the Chase Amazon card (and recently, the upgraded Prime card) for about 10 years, and I don't think I've ever received a CLI.
I agree with the above post. If your profile can absorb adding another account (over just a HP CLI) it makes the most sense to add another Chase card... preferably one that is known to provide a strong SL which can then be moved to whichever product you currently have.