In the jar of a blender, combine 3 cups water, bananas, and sugar. Blend until smooth and set aside.
In a large bowl or pot, combine remaining water, pineapple juice, orange juice concentrate, and lemonade concentrate and mix well or blend with an immersion blender. Add banana mixture.
Divide the mixture evenly among 3 freezer-safe containers or gallon-sized zip-top bags and freeze for several hours or overnight (at least).
When ready to serve, place 1 container of banana mixture at a time into a drink bowl or jar and pour 1 liter of chilled ginger ale or Sprite over the banana mixture. Mix with a spoon (or immersion blender) and serve immediately.
If desired, you can garnish with frozen berries.
Notes
Makes about 30 8-ounce servings to 60 4-ounce servings. Feel free to cut it in half if needed, or simply prepare just one bag and 1 liter of soda and save the rest for another occasion.