I guess you have been using box dyes?
If you go a little lighter than your natural colour, and add some highlights the greys will blend nicely. You can also use direct dyes to make them less starkly white as you get more, they don't take well to grey hair so you still get a highlighted look
I think a few rounds of color remover will be the best route, get all the old reddish brown out first. What colour is your natural hair?