I would definitely go more highlights. Your hair dresser can add honey tones as well as icy blond strands for greater dimension. Plus, highlighting will look more natural than just bleaching your whole head.
Get more highlights. If you dye it all at once, you're hair is going to be so beyond dead and depending on how light you go, you could have a lot of your hair fall out. At least that's what one of my hairdressers told me once upon a time.
It's a longer process obviously and you need to have patience, but it's a lot better than dying it all at once.