1. Place the partially-thawed, frozen, sliced strawberries into a blender. Add coconut milk. Blend until smooth, stopping to scrape down sides, if needed.
2. Pour into a punch bowl, or other large container.
3. Add 3 cups pineapple juice, 3 cups club soda, and 2 cups light rum.(You may substitute 2 additional cups club soda for the rum for a non-alcoholic version).
4. Add sugar or sweetener to taste, if desired. Stir until blended.
5. Ladle into glasses filled with crushed ice and serve immediately.