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If I'm currently under review for an app, and that bank already pulled my credit, will they be aware if I do an additional app and pull somewhere else's? Or since they pulled my credit already, they won't see that update to my inquire count?
If they already pulled your report, there's no way that they would see another inquiry unless they pull your report again for some reason which I don't think would happen too often. Not for something like a CC anyway. If you were talking a mortgage that was drawn out for a month or so, I could see the lender giving you a HP initially, then a SP a month later to just sort of check in on the profile to ensure it was still the same.
I'm not sure who the first app is through, but Chase has been known to SP while evaluating your app so they would see the new INQ.
It's possible, as during underwriter review they can do a SP on the credit report to see if anything is changed.
It happened for me once, when I applied for a credit union card and conditionally approved( pending income verification); assuming my application was approved, I applied for other cards from other banks.
But when I submitted POI, credit union declined to move further with my application citing recent inquiries on my CR(apart from inquiries, I did not have any negatives on my report).
Hence if you applied for a particular card in need, it's better not to apply other cards until the application in question is completely approved.
As above poster mentioned, I have seen many people reporting on Chase doing SP during the time period application was pending.