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I hear of so many on here who negotiate these deals all the time. Do they switch you over to a better card without HP'ing your report? And is a CLI automatically involved along with the extra perks? Who qualifies for this bargaining power?
You call the bank and ask to switch to a different product. There is no HP. There is no CLI. There is not really anything magical about it. Its easier to do with some banks or credit unions than it is for others.
The banks and card issuers aren't all identical so generalizations aren't going to mean much. If you're curious about the specifics then look into threads on specific cards that you're interested in PC'ing from and to. Some of them don't actually PC and close the old account and open a new account.