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Questions that will be asked before anyone can provide advice:
what is your current utilization? total and indiviual
what does your profile look like? scores, AAoA, baddies, inquires, ect.
That being said the catch 22 of credit is when you need credit you can't get it so there is a possibility that you will not get approved if your utilization is too high and/or your scores are too low.
CCT Experian offers a trial 7 day membership for $1. It will give you all 3 FICO scores and you can cancel it before the 7th day. I kept the membership causes they offer you 50% off if you keep it. It gives you daily EX updates and monthly TU and EQ.
I don't think you should be looking for another card to try and lower your utilization. Two things I'd do first:
1 - Pay down your balances. Get your overall utilization at 29% or less then set your next goal at 9% or less. You'll probably see a nice 10-20 point score increase from hitting the 29% bench mark and again if you can get to 9%. As someone above said, let us know your utilizations on each card. Ideally you'll want all but 1 card to show a 0 balance... so I'd start by trying to get a couple of them to 0. If you have any that are maxed out and/or nearly maxed out you should reel those in as well.
2 - Request CLI's from any of the cards you have that won't result in a HP. There's no harm in being denied CLIs if they are only SPs. Even if just 1 or 2 of the cards you have gave you a slight CLI it would help drop your utilization a little. Keep in mind though that you could get denied for CLIs, especially on the cards which you are showing higher utilization on.