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Welcome, @Anonymous.
I'm counting three cards (Discover, Credit Union, and Capital One Platinum). What's your fourth card?
Note that adding accounts will likely cause scoring decreases in the short term. And scores in the 630s don't really put you in a good position for approvals. I'm glad you're waiting to apply. Just let things age and let your current cards begin to work for you.
If you can let your newest account reach a year in age, there should be a decent scoring bump. Granted, you'll lose those points as soon as you add another account, but the increase might be enough to position you for a Chase card.
Your inquiry situation is fine. As long as you're not applying willy nilly, your inquiries will remain in check, and you won't have to worry if an application causes more than one bureau to be pulled. I'm a fan of one card every six months. That should be enough to keep you from being declined on the basis of new accounts or inquiries.
Total CL: $321.7k | UTL: 2% | AAoA: 7.0yrs | Baddies: 0 | Other: Lease, Loan, *No Mortgage, All Inq's from Jun '20 Car Shopping |