In illustrator I always duplicated the image so in this case you would have three copies. Decide which color you are doing and changed the other colors to white and the color you are working on to your spot color. Then to extend the gradient sliders farther out for each color so that you get overlap and minimal shirt showing through. How much is something I just do by eye and it really does not take long at all once you have done it a couple times.
There could be a better way but this is how I handled it.
So something like this?
you have green and blue at 100% in the same place. Find the areas that are solid color and stretch the other colors so they fade out right before it. You can move the slider to select the center point of the gradient and move it closer to the solid area. In the middle between two solid spots, your gradients should be at least 60% or more (to avoid the shirt showing through).
pierre
