Hair advice for a beginner in coloring!

Hi everyone,

So my hair is naturally brown-black (looks black indoors and dark-brown in the sunlight).

For the past 2 years I've been coloring/lightning my hair to a medium brown (copper toned) color with permanent dye. I also have about an inch of my black roots coming back in at the moment.

This is what my hair looks like now (for some reason the photos wont attach, so here's a link):
https://drive.google.com/file/d/0B7KnpdJPVxdpQ2huQW9iNDVVZkE/view?usp=sharing
https://drive.google.com/file/d/0B7KnpdJPVxdpRm5UdUI4Z0hnNDQ/view?usp=sharing

Anyhow, I'm a little tired of my medium brown hair and I want to try something new. I want to color my hair darker with subtle hints of burgundy. I'm not looking to become an artificial-tomato red-head. Basically, the color I'm after is dark brown/black with a purple-red undertone.

Basically, this is what I'm going for (also attached):

Is it possible to do this with already chemically-dyed hair that is medium brown? Or should I wait for my natural black hair to grow back?

I'd also rather not go to a salon and pay hundreds to change my color, so is it possible to do this at home?