Box dye over salon dye ??

Hair history- red high lights, blonde high lights, then dyed my hair red, then cut and dyed my hair dark brown in September. ( I'm pretty sure the highlighted parts were chopped off) . 
I was told I can't dye my hair a few shades lighter w/o bleaching it due to having salon dye in it.  I want to use a box dye , I'm not sure which one yet . So is it necessary to bleach my hair to go 2-3 shades lighter? Or can I just go straight in with the box dye