In a medium-size mixing bowl, combine the mango, papaya, cucumber, and crab. Portion greens onto individual plates. Divide the diced fruit, cucumber, and crab mixture evenly among the plates. Next, divide the raspberries over the salad.
In a small mixing bowl, combine dressing ingredients. Whisk until blended. Discard any cartilage from the fresh crabmeat and place in a separate mixing bowl. Spoon the dressing over the salads and top with toasted almonds and coconut. Drizzle plate with balsamic-rum reduction. Garnish with a sprinkle of parsley.
Lilikoi Dressing
Whisk together all ingredients in a small bowl. Cover and chill before serving. Yields 2 cups.