Start by sterilizing jars and lids. This takes a little while, so I start this 1st. I place my clean jars in my canner and cover with hot water. Bring this to a boil and boil for at least 10 minutes. Remove jars when ready to use. Pour some of the boiling water from jars back into canner and keep the water boiling so you will be ready to process jars of jam. In another small pot; sterilize lids in gently boiling water.
Prepare fruit; peel and remove seed from peaches, coarsely puree. I use my food processer and it works great for pureering peaches and chopping cherries. Just don't totally liquify the fruit. A little juicey won't hurt. Drain crushed pineapple and drain and chop cherries.
Transfer prepared fruit to a large, heavy-bottomed pot. Add the sugar, lemon juice, rum, and butter. Bring to a full rolling boil over medium-high heat, stirring constantly. Add the pectin and return the mixture to a full rolling boil. Boil hard for 2 minutes. Remove pot from the heat and skim any foam from the surface with a metal spoon.
Ladle hot jam into hot sterilized jars, leaving 1/4-inch headspace. Wipe rims of the jars, cover with lids, and screw bands on until just barely tight. Place jars on rack in pot and cover completely with boiling water. Cover pot; boil over high heat for 10 minutes. Turn off heat, uncover pot, and allow jars to rest in water for five minutes. Remove jars from pot and allow them to rest undisturbed on countertop for six hours or overnight. Preserved jam will keep for up to one year in a cool, dark place. Unpreserved jam will keep in the refrigerator for about six months.