I don't think there is any problem with applying for additional cards (personal or business) as long as you wait at least sixty days between apps. And, apparenlty the bank systems consider a "business" card app as in a different category than a personal app so if you have a personal card and apply for a business card there is no need to wait even sixty days. Note that this applies even if your taxpayer ID # for the business card is your Social Security Number and your business is a kitchen table one.
As to what happened with my several apps, no, I never got a duplicate application letter. I don't recall the exact timing, but I believe I had one personal card account open and then applied for a new personal card, which I got, and then a business card. Of course, I close accounts after they have been open for a while. Why pay that annual fee?
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