In blender container, combine bananas and limeade concentrate. Cover; blend until smooth.
In large nonmetal freezer container, combine banana mixture, rum and 2 cups of the carbonated beverage; mix well. Cover container; freeze at least 5 hours or until frozen.
Twenty to 30 minutes before serving time, remove mixture from freezer. To serve, add remaining 2 cups carbonated beverage to banana mixture; stir until slushy. Spoon into glasses. Garnish as desired.