Best way to dye highlights?

So I had a question earlier about dying my highlights to my natural hair color so they don't look so bad, but I phrased it wrong. What I meant to ask is, is there a way to dye just the highlights without getting dye in the rest of my hair? And is there a time I'm suppose to wait to dye it again to prevent damage? Also, since I have really thick black/brown-black hair and the highlights I have now are like a coppery reddish color (ugh- it makes my hair look damaged and it was done professionally), would a dark brown dye still look dark brown, or would I have to bleach it first for it to actually show up as dark brown? One last thing- any good dye recommendations? Thanks:)