Add the pineapple juice, orange juice, and lime juice. Stir well to combine.
Pour in the grenadine and gently stir until the color is even throughout the mixture.
Refrigerate for at least 1 hour before serving to let the flavors blend.
Fill glasses with ice when ready to serve. Pour the punch mixture over the ice.
Garnish each glass with orange and lime slices. Add mint sprigs if desired.
Notes
The recipe serves 10-12 people and can be doubled for larger groups.Store any leftover punch in the refrigerator for up to 24 hours.For a stronger drink, add more rum. For a milder version, reduce the rum or add more fruit juice.Fresh-squeezed juices make the best punch, but bottled juices work too.Make a non-alcoholic version by replacing the rum with ginger ale or lemon-lime soda.