You make a good point. I have heard from reps at a couple of banks like Citi and Chase that having more than five personal cards could be problematic. So, I assume that having more than five cards total could also be problematic and that they should somehow be split up between personal and business.
I am now reconsidering. Maybe I should go for five personal and five business at the same time! ^ Two hundred thousand bonus miles.!
Or maybe, even I don't have than much nerve--and time to manage credit card accounts.
By the way, the idea that the banks are making money on all these accounts is, IMHO, incorrect. If I open an account get 20K (estimated coast to bank $200) bonus and only use the card to charge, say, $300, it appears that the bank gets, maybe, tops, six bucks in interchange, no interest (I pay in full) and does not get its bonus back.