Chill rums and juices ahead for best results. Add light rum, dark rum, and spiced rum to a large punch bowl or pitcher.
Pour in orange juice, pineapple juice, and lime juice. Stir in grenadine and simple syrup until well mixed.
Add plenty of ice to keep the punch cold. Top with club soda just before serving and stir gently.
Float orange slices on top and garnish with a sprinkle of nutmeg if desired.
Notes
Adjust syrup and grenadine for sweetness. Try vanilla rum for more vanilla flavor—skip or reduce spiced rum so flavors don't clash. Fresh orange juice is best, and a little nutmeg brings warm aroma.