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So a small bit of annecdote may have been shared before. I have not been able to get a AMEX CLI on my revolvers for the past 2+ years with out them requesting 4406T, which I have no problem and have filled out many times but it seems that they don't process the transcript request unless I call them multiple times. Then, the one time I did that, I got a $1,500 increase since my CL's were already high enough by their standards. Blah!
This time what I did was move my available credit around to other cards, online leaving one of the cards with a $8,000 CL, and after about a week of moving limits I requested a CLI on that lower limit card and SURPRISE! Went from $8k to $15,000 (Which is what I requested). They obviously did not take CL from any other cards, so it was a net gain of $7k available on AMEX (for revolvers). FYI these are all personal cards.
Here is my before and after moving limits, and the increase -
Amex Platinum Charge - N/A
Amex Zync Charge - N/A (yes I actually still have one lol)
Delta Skymiles Platinum - $18k --> $24k (moved from SPG)
HHonors Ascend - $38,500 --> $44,000 (moved from SPG)
SPG - $19,500 --> $8k (moved to other revolvers) --> $15k (after CLI request about 10 days later)
Now my total revolver CL's are $83k with AMEX, whereas I could not budge on my current revolver exposure before this and the HHonors card had a good limit only because it transferred over from CITI with that limit.
Although directly related to your question about a workaround, this thread might offer some insight:
https://ficoforums.myfico.com/t5/Credit-Card-Applications/Citi-Costco-4506-T/td-p/5265653