I have three Citi cards, one is the AAdvantage MC, a Dividend MC and the new AAdvantage AMEX. I had a second Dividend card but never used it. I had it as a spare since, initially, my original Dividend card only allowed for a $500 credit limit and thought that if I ever wanted to go above $500 on a dividend type card I could simply use the second one.
However, when the Citi AMEX arrived the other day, it had a letter attached which said they closed out that second and inactive Dividend card so that I could have more credit available on the AMEX. So, it seems to me that although you can have multiple cards, they still limit your overall credit amount by spreading it over the cards you have. Since that time, I have applied and was granted for additional credit limit to the Dividend card.