The trick to having each bridesmaid wear a different color (or totally different dresses) is that the dresses must have at least one similar trait, which pulls everything together, making the look cohesive.
Where should your bridesmaids be similar? Depending on the style you want, you can start with choosing one of these details: fabric; dress length; color tone (pastels, brights, neutrals, one color, etc.), style (vintage, simple, romantic, bohemian, glamorous, strapless, etc.). It will be trial and error with your girls, but, I think it's worth a try for the beautiful effect that can come from it.