Regardless of what you do, please use colour remover before hand on the box dyed hair to remove ANY dye from the hair, it will prevent any 'nasty surprises' during your process, bleaching out box dye is very different to bleaching out professional colour... VERY DIFFERENT RESULTS, it'll make the process much smoother for you too because then all you'd have to do is go over with your base colour with a professional range then do your balayage and tone, much less hassle for you then. Honestly wouldn't try and work around/with the box colour as a base to begin with, i'd much prefer removing it so you can use her hair as a blank canvas and put your level 5 colour then on the grey/roots or wherever you want that placed, then using bleach do the balayage part and tone to finish off,
I'd start by colour remover all over first anyway, do that twice because you have to do it twice to remove all molecules and to stop it from re-oxidizing, then when that's all removed you should be left with her natural hair (box dye uses peroxide as you know so obviously it's not virgin hair and is probably lighter than it is naturally, but you'll be left with somewhat of a blank-er canvas.
I'm not sure if you can colour straight after colour remover, so check the manufacturers instructions, and follow it accordingly. you may need to wait, but with modern day ones should be able to start immediately after, if not i'd look for a better colour remover, they're less damaging, that Pravana colour remover thing is supposed to be good *i forget the name, but i know its available in the US and its a 2 step thing, it doesn't lift hair either, just removes artificial dye
Then I'd begin by doing your base colour and then your balayage, personally i like to do them separately as in do one, wash off, dry then do the other, but if you want to do them both in one process you certainly can!
then finally tone it, hope I've offered you help!