In a blender, combine 30ml of white rum, 30ml of aged Caribbean rum, 30ml of navy rum, 22.5ml of pink grapefruit juice, 22.5ml of lime juice, and 7.5ml of allspice dram.
Add 7.5ml of honey syrup, 7.5ml of demerara syrup, and 210ml of crushed ice. Blend, pour into a chilled double old-fashioned glass, and garnish with a lime wedge and mint sprigs.