I too have broken a blade when trying this - I believe it was a cast blade.
On a recent renovation I faced the problem of the blade pulling to one side quite severely - so I tried Tom's approach of using CA glue on a thin washer on the inside scale opposite to the problem. By filing a wedge I was able to see the improvement - but it needed a bit more so I put another washer on top and did the same again with an almost perfect outcome. As Tom continually points out - a little at the pivot can be a lot at the wedge.
Incidentally, I found using CA accelerator very useful. I used a small piece of rod to position the washer in place - then a squirt of accelerator and quickly removed the rod before it had a chance to set - and the washer was firm enough to file right away.