I have no experience with Citi, but when I wanted to make a purchase on my Chase Amazon Visa that was larger than the credit limit on that card, I called them and they gladly moved credit from a different Chase card I had instead of doing a credit pull.
I first asked for the credit increase over the phone, and was told that would require a credit report and she asked if that was okay. I said I'd rather not, and asked if it was possible to move the credit from a different card instead. Pretty painless.