Yes you can, but you cannot just put brown hair color on it. When you bleach all color or pigment is removed. To get the perfect color you much fill your hair with all missing colors. So if you want your hair brown, you must first put a color without a developer on your hair dry.
Does brown dye wash out bleached hair?
No, it won't. The porosity of your hair from bleach will make it even less permanent. When you bleach hair, you strip the pigment.
How can I dye over bleached hair at home?
https://www.youtube.com/watch?v=Tjz3iQLtaW8
Can you dye bleached hair brown?
Dyeing bleached hair back to brown isn't hard, but it does involve more steps than your average dye job since you'll need to add warm tones back into your hair. Don't worry though—below we'll walk you through everything you need to do to transform your hair step-by-step.
Can I put brown box dye over bleached hair?
Yes, Dying your hair immediately after bleaching it is ok, but it's best to stay in a color range that is similar to what you are bleaching it to. Keep the water temp cool, and make sure you condition the hair.