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@SouthFayetteFan wrote, you can apply for the SW business and personal card on the same day if you can manage the combined minimum spending requirements, but
you absolutely must apply for the SW business card first.
Start applying early during regular business hours of a non-holiday weekday in case you need to call Chase reconsideration or verification departments.
Apply for the SW
business card
first because Chase has an informal 0/30 rule that denies approval for a business card if you've had any other credit card applications with Chase in the past 30 days. If you applied for the SW personal card first, that would count as 1/30 and push your business application out another 30 days. Make sure the business card is approved before you go for the personal card. If you aren't auto-approved and perhaps got the we'll let you know in 30 days message, call the automated status line at
1-800-432-3117 after an hour to check the status of your application. If you still aren't approved call recon at
1-888-270-2127 to get it approved. (If you’re applying for DH, make sure he’s on board to possibly call into Chase.)
After that first card is approved, use a different internet browser or an incognito window for the second application for the SW
personal card, otherwise Chase may combine the apps thinking they're accidental duplicates. If it isn't auto-approved, call the automated status line after an hour, and if you still aren't approved call recon to get it approved.
Conventional wisdom says double dipping a business card and a personal card on the same day does not combine hard pulls; Chase will pull two credit reports for the business line and the personal line of credit. But at least double dipping will get you two cards with potentially enough bonus points for a CP, and you can figure out your spend with them in hand.