It is possible. And yes you can do this at home.
I have naturally redish hair which for 10 years I coloured iced brown. 2 weeks ago I decided I wanted to go a light ash brown and achieved this myself at home.
Step 1- Don't wash your hair for 2 days to let natural oils build up, this help limit damage from bleaches.
Use a colour remover such as L'oreal perfect blonde (use maximum for stripping all colour out)
Next I rinsed it with warm water until it ran clear and let it air dry.
I purchased Garnier belle colour 7.1 (lightest ash brown) and waited 40 minutes for coverage to be done. When I rinsed it it had a slight green tinge, However I diluted 6 asprin in a glass of warm water and massaged into my hair, waited 10 minutes and rinsed and all the green had gone. The water comes out a slight greenish colour (The asprin removes copper from the hair that gives it the green effect)
Deep condition and wait for about 48 hours, then get a highlight kit and place highlights wherever you want them, this gives it a really natural and summery look. The reason for the highlights is that by stripping the hair in the first place you remove the natural multi tones in the hair, so replace them with a light bleach highlight.
I done all of this myself and it looks gorgeous, and it cost me less than $25.00 to do. It is a little time consuming, though after the 1st time its just a matter of root touch up and that takes no more than 20 minutes a month.
So yes, you can achieve it, it may make your hair a little dry, but some olive oil through it twice a week for a month, leave for 15 minutes and rinse will sort it out 100%
Hope this helps =D