Want more red

I used a light reddish brown dye and of course it came out dark because of the hairdye buildup I have but that's okay cause i actually like it. The problem is I can't really see any of the red. I have a lot of red undertones in my hair naturally. Do you think if I put a light red over it (I know it won't turn really light, it would end up being dark) would it blend in with the brown so it would look reddish brown? That's the color I want to end up with. Or would it make my hair all red? What about the next time, I buy a light brown dye and a light red dye and mix half and half. Would that turn out better then the one box of light reddish brown did?