Set a large strainer on top of a plate or large flat bowl. Set aside for just a moment. Drain out the juice from the cans of fruit. Add the pineapple, fruit cocktail, and mandarin oranges to the strainer.
Cut the cherries in half and add them to the strainer. Using a spoon, spread the fruit out in the strainer so it’s not lumped together. Let the fruit sit in the strainer for 2 to 3 hours (or more) if you have time, so that all of the juice is completely drained from the fruit.
Transfer the fruit to a large bowl and add the marshmallows, and Cool Whip. Gently blend in the Cool Whip. Garnish with maraschino cherries with stems. Serve chilled.