Can I go platinum in one go?

Hi all. So after a few hair disasters I'm after going platinum blonde. End of April I had my hair bleached which went great but fast forward a few months I tried doing my roots at home and ended up ginger despite toning. In a last ditch attempt to make my hair somewhat normal looking I used a temp ash dye and went green lol. As I couldn't go out with the green hair I ended up putting a permanent auburn copper dye on. I've since been to hairdressers for a cut and despite everything the hairdresser said my hair was in good condition. I've since used Scott cornwalls decolour remover and have been left with blonde once again but a medium blonde not the bleached blonde I was. I'm planning on getting it done at the salon to save any more disasters but wondering if after bleaching again I can tone it to the white that I want without having to bleach again. Pic of my current colour