Drain pineapple, reserving 1 ½ cups (375 mL) juice. In blender container, combine 1 can drained pineapple, ¼ cup (60 mL) reserved pineapple juice, ¼ cup (60 mL) orange juice, ¼ cup (60 mL) coconut milk and ¼ cup (60 mL) rum; cover. Blend on high speed until pineapple is puréed. Add ice; blend until smooth.
Pour into 4 tall glasses and serve immediately. Repeat until all ingredients have been used.