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I'm not sure about any concrete answer here, but I can tell you that I got approved for $15k on the cash magnet and $20k on the SPG without any HPs. I used the targeted offer in my account under the "my card offers" link. I would suggest looking at whatever cards they are offering you, and hope they don't do any HPs.
Hello there
I currently have two AMEX cards (Gold Delta & Hilton Ascend). It has been my experience that for CLI's and applying for another card, they do not do a HP. I have requested a CLI and been denied after the first 3 months of my Gold Delta card and it was not on my credit report. When I applied for the Ascend card it also did not show on my credit report. I recently requested a CLI on the ASCEND and they doubled the limit. I have also not had that appear on my credit. I believe everyone could be different, but it has been my experience, and that of others on these threads, that they do not do HP's for the existing customers.
Hopefully this helps.