I always seem to have trouble removing any semi-permenant colours from my hair. I've been using a pre-lightener but after 4 hours it turns the colours to a very kind of illuminous effect. If it makes it any easier my hair has either (from what it was dyed first to what it is now)

Bleach --> blue --> red --> black (permanent)
or
Bleach --> blue --> red

It has no problem getting rid of the black permanent colour but it seems really stubborn when it comes to the directions colours I use and barely lifts anything out even after about 4 hours. Would it help if I got two bleaching kits? Or do I need to try something else?

Thanks :-)

What bleach are you using? 4 hours is going to do a hell of a lot of damage to your hair and scalp by the way.
Some colours are harder to get rid of than others. Pinkish purples are a real pain in the ass to get rid of without going neon pink in my experience. And plum has a tendency to go green.
I find it's much easier to bleach a colour out if it's already pretty faded, it tends to skip that neon stage, maybe you could give that a try.