Sometimes a bank may be hesitant to approve you for a card because you may have recently gotten a card from the same bank. For example, a bank such as Chase, may approve you for one card every 6 months. I personally at times have gotten around this by calling them on the phone and moving some of my credit from one of my existing Chase credit cards to the new one that I am applying for. With Chase however, you need to make sure your application will not be barred by the 5/24 rule.
Generally, a bank is more apt to approve your application if they are not extending you additional credit but rather just transferring some of your existing credit to a new line.
BTW, for me this has worked with applications for my Chase Marriott Rewards Premier card, and my Chase IHG Rewards Club Select Credit Card For Rob, it has worked with applications for his Chase Marriott Rewards Premier card too and his Chase United MileagePlus Explorer Visa. More recently, I have employed this strategy to push through applications for the Chase Sapphire Reserve card and both Rob and my Barclays JetBlue Plus MasterCards
The current phone numbers (they sometimes change) to call to reallocate your credit are as follows:
Amex-877-399-3083
Chase-888-609-7805 or 888-270-2127 (800-527-7415-for the Ritz Carlton card)
Barclays-866-408-4064
Citibank-800-695-5171
Bank of America-800-354-0401 or 866-505-7481
Capital One-800-625-7866
Please let me know if you use one of the above numbers and they no longer work. Thanks!