Peel outer leaves off of cabbage and radicchio and shred them with a sharp Santoku or chef knife. Don't worry about making them too thin.
Wash and dry kale and remove greenery from the stalk. Chop to about the same thickness as the cabbage.
Wash and drain cranberries, then slice them into rounds with a small paring knife.
Segment the pomegranate and set aside.
In a large salad bowl, toss kale with a tablespoon of vinaigrette and allow to marinade for about five minutes.
Add cabbage and radicchio and toss with a few more tablespoons vinaigrette. Sprinkle sliced cranberries and pomegranates and present at the table. Toss salad one more time before mounding it onto plates.