Pour in the white rum, dark rum, banana liqueur, blackberry liqueur, pineapple juice, lime juice, and grenadine. Cover and shake vigorously until chilled, about 30 seconds.
Fill a hurricane glass with ice and strain the cocktail into the glass. Garnish with fruit if desired and serve immediately.
Notes
Blackberry liqueur can be hard to find sometimes. Chambord (black raspberry liqueur) has a close enough flavor that it can be substituted instead and your cocktail will still be delicious. Blackberry flavored brandy would also work.
Do not use spiced rum in place of dark rum. They are two very different spirits.