Combine the soy milk, juice, banana, strawberries, blueberries, and peaches in the carafe of a blender. Cover and refrigerate overnight or up to 8 hours.
In the morning, or when the fruit is partially thawed, put the carafe on the base of the blender, start at the lowest speed and slowly accelerate to medium until you achieve a vortex. Blend on medium for 1 minute. Increase the speed to high and blend for an additional minute. Serve immediately.