ashy brunette wants to go red

Is it possible?

My hair is pretty ashy medium brown (as in, when I compare my natural colour to hairdye swatches, it has a fairly greenish tone).

I know that the best colours for me are ashy tones, brown blonde, etc.

But does this rule out red for me (except in small doses)? I am a huge fan of red hair, and used to always do a level 2 semi-permanent hairdye in a subtle auburn to good results. I love copper reds, but I'm worried that my ruddy complexion rules out any chance I have of going red.

Suggestions?