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Personally I would wait until 6 months after you opened the last acct and give them a call.
Explain the situation (calmly) and ask if there is anything that can be done to increase the limits to be more in line with the rest of your collection.
You're getting ahead of yourself, I think. I doubt you've reached your internal limit with only $3500 in current limits. Putting together a six month history of good use on the current cards will help. $2,000 flowing through the checking account helps too. The major fear people have about the CSP stems from the fact that Chase doesn't like to be anyone's first $5k card. Not a problem for you. I think you're in good shape for a CSP approval in June, even at your current Chase limits.
Im also planning to app for a Chase card and have been doing a little research, myself. Not sure if its ok to post this, but buried in this thread is some pretty good info about Chase underwriting that might help you.
http://www.fatwallet.com/forums/finance/1237474/
hope this helps and good luck.....
I was told by multiple people that the credit card department does not look at bank accounts when approving credit cards. You can have a banker help you out but you need to have at least 10000 in an account, and it still does not guarantee approval. 2000 a month really is not that much to them. If you increase the limits on current Chase cards, your odds of getting the Chase Sapphire Preferred are very slim. I would keep those limits where they are and wait until at least June or even September to attempt the Chase Sapphire Preferred.
Using the cards and paying them off is the best option. They are not too keen on people who have opened multiple accounts, unless history is fairly long.
That FW thread started with high potential and never amounted to much. Kind of a shame, really.