yes, I too have a few business and personal cards. At one point I had to call and reallocate to get approved so the rep let me know what overall credit liability chase was comfortable with. I then voluntarily cut some cards I didn't plan on using too much to $5000 and the next app was auto approved. I imagine if my income goes up they would re-evaluate me for more, but knowing the $$$ i'm good for, keeps my apps auto approved.
I was also asked about the large number of recent apps one time and I had my list of recently canceled cards in front of me and I told them I like to re-evaluate my cards a couple of times a year and get rid of cards I don't use much, to make room for new cards. I then read a few examples and dates (which the analyst probably had in front of him on the same report showing my new cards) to let them know I am cancelling cards and not just applying for more.
A good excuse is well airline A bought airline B so I don't think I need airline B's card for much longer...or even better "I'm disappointed in CITI or AMEX and am cancelling a bunch of their cards, so I can get more of yours"

You can probably have 12 chase cards if the CL is allocated right and they are applied for over time at a steady rate