Can I use a color remover on my hair and THEN bleach it?

Anonymous
I used to have my hair blue. Then I dyed it black. This was about a month and a half ago. I want to go back to blue hair. Right now, my hair has since faded a bit from the black hair. Yes, a majority is still black but I have some parts and streaks of a medium brown color. I bought L'Oréal Quick Blue bleach. It says it lifts up to 7 levels. But I'm not sure it'll get me to the blonde that I need to dye it blue. So I was thinking maybe I can use a hair color remover (which, yes. I know also includes bleach) and then use the Quick Blue with a 30 developer. Would I work?

As as far as the condition of my hair, it's healthy. Really soft. I deep condition my hair twice a week. And back when I had it blue, I deep conditioned four times a week. Plus, the dye I use is from Artic Fox which has conditioner in it already.
Can I use a color remover on my hair and THEN bleach it?
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