In a cocktail shaker or mixing glass, combine the light rum, dark rum, banana liqueur, blackberry liqueur, orange juice, pineapple juice, and grenadine.
Add ice cubes to the shaker or mixing glass, and either shake it vigorously or stir it thoroughly.
Fill a hurricane glass with crushed ice, strain the cocktail mixture into the glass, and add extra ice if necessary. Optionally, add a fruit garnish, such as an orange slice, pineapple wedge, or cherry.