Prepare a day or two in advance to allow the mixture to reach it's full slushiness. The alcohol will keep it from freezing solid. It's good to rough it up a bit from time to time with a fork, but not completely necessary.
This will keep covered in your freezer up to two weeks. We've never had it last even that long, however.
NOTE: The prep time indicated does not include the freezing time required.
Begin by making a simple syrup. Bring 8 cups water to a boil and stir in 3 cups sugar. Continue to stir until the sugar dissolves and mixes with the water (about 15 minutes). Set aside and cool to room temperature.
In a large bowl, combine the juice of 2 lemons, juice of 2 oranges, can of pineapple juice, frozen grapefruit juice, frozen lemonade and rum.
Once the simple syrup is cooled, add the juice/rum mix to the syrup. Stir and transfer to an air-tight container with lid. (I have a large Pyrex container that I use for this; a plastic ice cream bucket with a lid would work, too.)
Place in freezer 2 – 3 hours. Scrape/Stir/Mix and return to freezer overnight.
To serve as a cocktail - with an ice cream scoop, fill a cocktail glass half full with the frozen slush and top off with a little lemon-lime soda.
To serve as an after dinner adult treat – serve scooped/scraped into a small dessert dish with a demitasse spoon.