Most promo codes apply to new customers only, so you likely won't qualify for another once you use one.
That said, if there are different promo codes for multiple accounts at Capital One, you can usually stack multiple offers for one big pay day.
For example, if you're a totally new Capital One customer, then you can get both a Capital One checking account bonus and a Capital One savings account bonus by opening both a new Capital One 360 Checking account and a new Capital One 360 Performance Savings account.