Most of the time they will make you move credit around or close another card. If you want to keep the cards open have reasons for them that don't sound abusive (e.g. I like the Ink card for the no-forex, but I expect an uptick in domestic travel both personally and for the business so we want to match the spend with the partner's card).

After they go through their questions is the time to broach re-allocating credit. If that is a no go, then offer to sacrifice a different card.

Finally, remember HUCA is an option if you have an inflexible rep (Hang up, call again - "for some reason I was disconnected . . . ") Chase is pretty easy to deal with though.