Question about credit limits thru multiple banks

Hi all,

I have credit cards open with 3 different banks, and a pretty good credit score, but I seem to be bumping up against my limit when it comes to credit increases (perhaps based on my income?) I was wondering if closing a card with one bank (let’s say it has a 10k credit limit) would then cause one of the other banks to be willing to increase my credit limit up to that amount (or something at all) – I know that hurts my credit score, just wondering if my credit cap is per-bank or total.