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There's no harm in trying for a CLI (credit limit increase) if there's no hard pull or if a denial doesn't reset a clock that prevents you from asking again in the relatively near future.
However, with maxed out cards, there's little chance of CLI success. If requesting results in unwanted consequences, it's better to wait until balances are substantially paid down.
If you look at how utilization affects your credit, it is the total limits compared to your balances. My credit recently dipped drastically from 740 to 680 cause my ut went from 45 percent to 51 percent. Once you get over 49% util, it KILLS your credit. Understand that is the TOTAL amount of utilization amongst all cards.
So, if you have 4 cards, 10k each, whether you have 2 cards maxed, and 2 at 1 dollar balance, or all 4 cards at 5k, the result on your credit is the same (40k total balance, owe a total of 20k - 50% utilization)
I fixed this quickly by paying off the one card that I had maxed (did a balance transfer to a card with 0% interest for 18 months) and ALSO got a few new cards to increase my total limit and hence reduce utilization.
My score went back to the 700s in about a month. Opening and closing accounts is good for you credit, so, if you don't have the money, SMARTEST thing you can do is get a card with a high limit with will decrease your total utilization.
Welcome, @Anonymous.
Overall and individual card utilization both factor in. Individual card utilization is determined by the card with the highest utilization. Although overall utilization is the more significant factor, a maxed out card will hit you hard. In your case, you killed two birds with one stone by paying down the maxed out card. That reduced both your overall and individual card utilization.
Opening accounts will most likely ding your scores in the short term as your AoYA (age of youngest account) and AAoA (average age of accounts) will be affected. You'll recover in time, though. The exception would be if adding a card or three significantly reduces one's overall utilization. That would trump the new account penalty.
Closing cards tends to be more or less irrelevant to scoring, mainly because closed accounts tend to stick around on your reports for years. One exception would be if closing accounts causes you to have less than three open cards. Another would be if your oldest account drops off your report and your second oldest account is quite a bit younger.