It is possible to highlight hair that has already been dyed, but it's better to highlight using foils. Sometimes, at-home kits make hair appear brassy or not the color that was planned, so it's important to recognize the risks involved before doing it personally.
Do not dye hair dark and then try to color it lighter, because a lighter color won't change a dark hair dye. To make dyed hair lighter, strip the hair of its color, and then lighten it with the required color. Adding highlights to dark hair is a procedure that's probably best done at a salon.