Pour the rum, pineapple juice, orange juice, and lime juice into a 1-gallon drink dispenser.
Stir with a long spoon for about 30 seconds, reaching to the bottom so nothing settles unmixed.
Pour in the grenadine without stirring, letting it sink partway so the punch shows a sunset gradient in the glass.
Cover and refrigerate the dispenser for at least 1 hour and up to 24 hours.
Just before guests arrive, give the dispenser one slow stir to distribute the grenadine, then add ice to the fill line.
Fill punch cups directly from the spigot, then finish each with an orange wheel and a cherry dropped on top.
Good to Know
For the zero proof dispenser, leave out the rum entirely and add an extra cup of pineapple juice in its place; the ratio of sweet to tart barely shifts.