I will say though that If you plan on doing such a dramatic change with your hair like this, I wouldn't advise you to do it in such a small time frame, and I would advise you to leave a few weeks between dying your hair each time, unlike me!
I've made a video on my hair journey, explaining all the products used and my recommendations so I suggest you go check it out, as you might learn a few things, even if you don't actually plan on ever going from brown hair to blonde!