Won't affect you at all.
For example, I know 2 people who basically have had the same cards for over a decade with only minimal auto CLI increases done. Some of those cards are just 1-3k CL, and I persuaded one to apply for a new card a few months ago. He applied for the CSP, and was instantly approved for 30k. It just really depends on your income and credit history. Your current lenders may not always have the most up to date record on your income and financial situation.
JPMorgan Palladium (100k), AmEx Platinum (NPSL), AmEx SPG (46k), AmEx BCP (42k), Chase Sapphire Preferred (47k), Citi Prestige (31k), Citi Thank You Preferred (27k), Citi Executive AAdvantage (25k), JPMorgan Ritz-Carlton (21k), Merrill+ (15k), US Bank Cash+ (22.5k), Wells Fargo (12k), Bloomingdale’s (12.4k), Chase Freedom (5k), Discover IT (5k).