You can have multiple cards from a single company. If you have a high credit limit on one of their cards and they deny you another card, you can call and offer to restructure your credit limit to make room for the new card. Offering to reduce credit limit usually will help you get another card with them, without having to close your old account. I agree that instead of closing an account it is better to switch to another brand card which keeps the older more established cards on your record. When I no longer used my skymiles amex, and didnt want to pay the fee anymore, I switched it to a no fee open card by amex. When my chase sapphire card tries to charge me the $85 yearly fee, I will change it to a no fee card (after transferring all my points off of it)