@Anonymous, Chase is very sensitive to new accounts and inquiries. They might be OK at the time of your application, but they've been known to close new accounts if too many other cards are opened around the same time. They won't see your AMEX business account, but they will see the inquiry associated with it.
Another thing to keep in mind is Chase's 5/24 rule. That means when one has opened five or more cards within the past 24 months, applications will be denied. You're OK with 5/24 right now. The AMEX business card doesn't count because it won't show up on your personal credit report. And on October 1, your first card will no longer count against 5/24.
Also note that you're likely to see some score decreases as these new accounts report. This can be mitigated somewhat be keeping a lid on the balances that report. Keeping all reported card balances at 28.9% of their limits or below will keep lenders from becoming concerned. That doesn't mean you can't spend more than 28.9% of a card's limit during the month. But it does mean that you should lower its balance if necessary before the statement cuts.
If keeping all cards at 28.9% or below puts your scores lower than you'd like, you can improve them by lowering balances further. One card reporting a small balance (at least $5, but not much more) — with the rest reporting zero — will optimize your score. We call that AZEO (all zero except one). Somewhere between AZEO and 28.9% on all cards may be your sweet spot between an ideal score and convenience.
Because the AMEX business card isn't on your personal report and doesn't factor into your scores, you can be a little more flexible with your statement balances. The ideal thing here would be to pay your statement balance in full every month. If you're taking advantage of a 0% promo, make sure you take a big bite out if your balance each month. Never pay only the minimum except on a very occasional basis.
A more practical reason not to apply for too many cards at once is sign-up bonuses. It may be hard to meet the spending requirements if you have too many sign-up bonuses going at once.
