Technically, yeah you could dye it. But you might need to bleach it. And it might fade to a greenish color. And it might not be the exact color you want. Manic Panic is a popular brand of dye.
What's this for? It's a wig.
What's it for? To disguise yourself from yourself.
So what's it going to be then, eh?
Follow the cosplay twitter! @FyeahCosplay