Regarding core card, what was the reason... did you manage to get core card later on?In my opinion, firstly, the culprit here is banks reporting duplicate limits to CIBIL. Next comes the total credit limit debt exposure, which is overleveraging for SBI. I don't think the number of cards is the reason.
I have an SBI Cashback card, but when applying for a core SBI card, I was rejected twice.