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I have 6, Revolvers: BCP. HHonors Surpass, Delta, Charge: Zync, Corp Charge: Green. Sadly the Delta card is on the chopping block in June, just don't fly Delta anymore got it manly for the 50k miles signing bonus. Southwest is now my airline of choice. The Corp Green is my favorite but no rewards sadly, but at least I don't ever have to pay the Green one, work takes care of that. ;-)
I have heard you can have 1 each of the Charge cards, Not sure of the number of Revolvers. but they let me have 4. Of course you can add small business AMEX cards if you have bussiness so you can have many AMEX cards if you so desire.
(3) here - BCP, Platinum charge, Delta Reserve