Just trying to clear this up as this question happens a lot. Hopefully this’ll save some people from some serious frustration. Emphasis in neon green on the screenshots is mine.
You can only have ONE Capital One card if your card is the Capital One Builder Program card. After it graduates and becomes a regular platinum, then the rules are the same as they are for the regular Platinum card (see below).
From the T&C of the Builder Program:
If you have TWO OR MORE Capital One cards open, you will get denied when attempting to apply for the following cards: QuicksilverOne, Platinum, Journey, Secured.
From the T&C of QuicksilverOne, which is the same as Platinum, Journey, Secured:
You have have FIVE TOTAL Capital One cards. This includes all cards offered.
From the T&C of Venture, which is the same for VentureOne and Quicksilver: