Actually I just noticed you were inquiring about a business cards which I know very little about so none of what I said may apply. Having said that, I'd be careful closing too many of them. It will drastically shorten your credit history which will also affect your score. In fact, I'd only close the ones that you think you might want to apply to again to get a sign up bonus in the future.

Also, I don't think it matters how many cards you have, only how many you have opened in the last 2 years. If you just want to increase your chances of auto-approval, you could just have them lower your credit limits and keep them open. But like I said, if you ever want to receive the sign up bonus again, you'll have to close them eventually.



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