The BA, Marriott, Sapphire, and Ritz Carlton credit card are all Chase cards. I don't know whether you would be approved for the first one without effort, but you would most certainly have to call the reconsideration line and explain why you want the 2nd, 3rd, and 4th cards. Many people have been able to get 2 personal Chase cards on the same day by calling, I think some have gotten 2 personal and a business card, but that's pushing the limits. Chase has allowed me to have 4 open credit cards at one time, others have talked their way into more open credit cards. I would prioritize and space out applications if I were you.
The Frugal Travel Guy recommends that you apply for 1 personal and 1 business card from each major bank on any given application spree (Chase, American Express, Citibank, Bank of America, Barclays). Make sure you can meet the minimum spend requirements on all the cards on your list before you apply.