I'm stuck with the same problem, I bought a dark grey/green flight suit (US army) and I soaked it in bleach for 24 hours but it still isn't light enough.
What is the original colour? And As mentioned above fibre content is important Though rayon and linen and wool and even nylon dye pretty easily to )Overdyeing can create some really interesting effects. I have some olive green natural though mystery fibre fabric that I plan on making brown. To do so I'm overdyeing in red as red and green are complimentary colours and so produce brown when mixed.