grey hair

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It would make sense that the roots that are white are coming out brighter than the rest of the hair.  White just shows through the color better, and the rest of the hair has been dyed more times each time she had the roots done, so there's more color packed on there and it has become more porous -I could see it picking up more of the color for that reason too.  It also could be that the roots are more gray than before (her gray hair is all coming out now more than before).  This may mean she has to change what she does to color her hair, since gray is more resistant to dye, the same dye that worked on regular hair won't do the same thing on gray hair. 

I'm not a pro, so I'm not really sure what to suggest.  Gray is known for resistance to the dye, you can try to open the gray hair up a bit by putting the dye alone on the white parts only for 10 minutes before you put the dye mixed with developer on all the hair.  (Supposedly the ammonia in the dye alone is supposed to open up the cuticle with its alkalinity).  I'd test strand it though to make sure that will work, I haven't tried it myself.   Otherwise, you may just need to do the white parts with a color that has more brown in it so they don't come out so bright.   I'd test strand everything you want to try, it sounds tricky.