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This is only my opinion but you are better off without having any Barclays cards. The arrival plus as well as the uber card are both great cards but Barclays is a very finicky lender to say the least. They will CLD, cancel, etc... to you and not even give you a reason half the time. Just my 2 cents. But you have the CSP which is a fantastic card so no real loss.
CSP apprroovveeddd.
Called automated line this morning, its been 48hours btw. 30 day message. Said screw it and called recon line because im an **bleep**. Guys says, "im gonna send you a text code and some security questions" in a generic manner. Then says give me a minute while i submit for approval(my heart pounding haha). Comes back on phone, congrats youve been approved for $23,400, you'll see it in a week or two. 5 minutes later it shows up in my chase app, which i needed to verify thinking no way he said $23,400 lol.
BTW Barclay is almost always worth a recon if for no other reason than the UW are prone to giving real feedback on why the denial and what to target to improve odds for next time.
As has been alluded they keep a close eye on overall credit status and can be jumpy in response to an adverse shift in your credit profile.