VERY unlikely that you will see a CLI while you are revolving a balance w/Amex. It's well known they're skittish around balance carriers.
Not me, I won't carry a balance even on my 0% cards. I read a thread earlier by another user where he stated his wife's Amex has never gotten a CLI and she revolves a balance. Then I went to go dig that one up for you but I saw that it was actually you he was responding to so I won't bother linking it since you already got the scoop
Obviously YMMV, but they approved my 3x CLI when I had a balance on my card. I had maybe a $5-600 balance when I requested the 61-day increase from $2k to $6k. Approved no sweat. I hope they aren't wary of balance carriers, because I'm revolving a balance (~$1k) to take advantage of the 0% interest period. The way I figure, why offer that to cardmembers as an incentive, and then knock us for using it responsibly (~30% or less util)?
Who, here, has gotten a 3xcli or any cli for that matter...with a balance on their Amex?
I'll prob have a $1500-2,000 balance on my BCE by the time June rolls around for my six month 3xcli. I started revolving a balance in January. it's at 0%, so I fig'd wth! lol Planning to request $24.5k. It will 100% be paid off by August and back to pif on a monthly basis. I just hope Amex isn't punitive esp when they are offering me 0%. I'm just never in a hurry to pay off a 0% promo, ya know?
Current limit is $10.5k.
I had to look back at my Optima statement from last May to get my answer to your question, and my answer is: Yes, I had a balance of $411 when my statement cut on May 20, 2012. Five days later (May 25th), I requested my first ever CLI on my Optima card and since I was such a scaredy cat, I didn't ask for the full 3x. My CL was $4100 at the time and I asked for an increase to $9600 (an increase of $5500) and it was approved instantly online. And also on that same day, I app'd for the BCE and got approved for $4,000 starting limit. Amex gave me lots of love that day!
Now time to get that balance paid down some! Looks like the people who are revolving balances have them in the hundreds rather than thousands. Give yourself the best chance at a CLI while still taking advantage of the 0%!