My credit score is 790ish, wife is 760ish. We've each applied for 6-10 cards in the past 15 months, usually about 1-2 months apart, have not been turned down yet. Did have one or two cases where we had to reallocate credit lines from one card to another. Wild guess is 45% Chase, 25% Amex, 20% Citi, 10% Barclay's. I'll know it's too much when we start getting turned down. I wonder if Amex even does credit pulls for existing customers. I mean, the credit pulls must cost them something, no?