Your best bet is to apply for the new card before closing any accounts. If they reject you for the new card, you can call and they may offer to open the card if you close another account. At that time, they can close the account and open the new one at the same time.

No need to close accounts ahead of time. If you're approved, you'll get a phone call asking you to shift credit from an existing account to the new one.

You can also call chase and have them consolidate your credit line on one card.

I applied for both the Sapphire and Continental cards at the same time. Called reconsideration about the Sapphire and she just moved a portion of my line from an old Chase non-rewards card. Waited a bit and called about the Continental and the CSR wanted to pull another bureau. I declined. Called back later and got the same CSR from the first call unfortunately who was then more hesitant. I offered to close the old Slate for the new CO, which she did but the apps has gone to review. We'll see how that goes next week.

So 2 apps in 60 days may be correct but you may not want to do them at the same time. Normally I space my apps at 90 days so I'll just do one Chase personal each round I suppose.

Its not just the amount of cards you have but also the amount of time you have had it open for as well as the amount of credit chase has open to you, and the amount of credit on each card. I have about 4 credit cards from chase for about 5 years now and have no problem open new cards.

Also, from my experience personal and business are different and don't really effect each other.

Chase is known to be rather conservative. I was just turned down for my 4th Chase (CO), saying I had too many open. I only use UA Mileage Plus, but don't want to close my ancient Slate or Freedom because they are my oldest revolving accounts. Meanwhile, everyone else and their mother gives me ridiculously high limits (much more on a single card than all my Chase cards combined). Oh, well.

And surely you called to offer to move some credit line from one of the existing cards to this new card, while keeping all of them open?

I have 5 cards.

I have 2 Chase rewards cards that are not marketed anymore.. the Freedom Card and Marriott making it 4 personal cards plus a debit and 2 business cards. I am waiting on them to come out with another BA offer to apply for!