Removing green undertones from hair

In December I dyed my hair a spectrum of blue and teal, by early March I put purple over the top of my hair. Then by the end of March I put black all over it except on the back inside just to keep some of the teal.

It wasnt a great brand and I probably didnt have enough so it ened fading on some parts and not dying so I also have blotches of green and random blond and blue. They dont bother me too much but I dont want to put another dark color over it because Im planning on bleaching it again and making it a a bright color. My basic question is just what can I do to get this into a blank canvas so I can probably get an orange or blue color again? What should I do? What color should I dye it? If I bleach it will it just be a green and silver mess? Its pretty healthy and its grown out about 2 1/2 inches.