hair dyeing question of doom

so, I dyed my hair, (all 2 sq inches of it) with a cheap drugstore red, and it didn't come out half bright enough. I still have plnty ofdye, so I was thinking of just slapping anouther treatment on it, frying it, I know, and see if it lightens/brightens it like a motherfucker. I don't really care what color it turns out, I'd just rather my hair not actually fall out.

So, should I take advantage of it's chemically weakened state to get a brighter color, or will I end up bald? I'd have posted this to like "hairdye" orsomething, but I don't have time to find such a place.