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Yes they do, but you eventually reach an internal limit with Chase at which time you would have to transfer balances from other Chase cards in order to reach limit you are looking for with CSP.
FICO TU 754
FICO EX 761
FICO EQ 766
CSR 28K, AMEX DELTA 20K, CITI AA EXECUTIVE 38K, AMEX PLATINUM, CHASE AMZON 3K, AMZON STORE 3.8K, MACYS 2K, FREEDOM 8K, CO 6.7K, DISC 9K..... TOTAL CREDIT 154K
It's not all about credit score when getting approved for a product and the terms with which you are approved. The OP mentions people with "lower scores" getting approved for a higher limit than him. Those people with lower scores may have had a stronger profile though in the eyes of Chase. For example, you can have two individuals with a credit score of 710, but one has 15 years of credit history and hasn't applied for anything in years where the other has 7 months of credit history and 5 new accounts. It's important to understand that the entire credit profile is considered, not simply a score.
It's also worth noting that Chase uses their own internal scoring model. While you may have a higher FICO score than someone you know that applies for the same Chase product as you, there's no way to tell if their internal scoring model weighs scoring criteria different. If so, it's completely possible that while your FICO score is higher than someone you know, their internal Chase score could be higher than yours.