Sample Goals

My hair is naturally dark brown. I cut off a sample of my hair and –using a bleaching kit I got at the supermarket–managed to get it to a medium (strawberry) blonde in 6 applications. However, my goal is to eventually get my hair to the color of platinum blonde.

So my question is this:
Based on the color change achieved so far, is dying my hair platinum blonde possible?
2/3 of my hair, which is 7 or 8 inches in total from the root in length, has remnants of black dye; will this hinder it’s ability to go platinum?
In response to Nancy H. –

Thank you very much for your advice, however I want it to look artificial. That’s why I asked the question; to determine if that nearly white blonde is possible…