I applied for the Hawaiian card and the Frontier personal card 2 weeks after getting the Hawaiian personal and 3 months after getting the Choice and Wyndham personals. I was approved for the Frontier personal after lowering my HA personal to $5K in a reconsideration call. That's 4 personals open now with $5K CL each, which I believe is the lower limit for the cards.
The rep told me there is no limit on the number of cards but rather on the total credit line you have. They also thanked me for "using" my card even though I sock drawer after making spend.
The HA Biz card is a rough one. I used a 35K app online and for some reason the link I used triggered a security flag. I'm having to send in copies of my drivers license, SS card, US passport, and a mail. But nothing requested about the business like business license, etc.
I don't know if the CL they give a person includes the Biz CL but if I apply for the Jet Blues I may have to cancel a card first.
Barclays is still fun.