Bring boiling-water canner, half full with water, to simmer. Wash jars and screw bands in hot soapy water; rinse with warm water. Pour boiling water over flat lids in saucepan off the heat. Let stand in hot water until ready to use. Drain well before filling.
Stem and crush strawberries thoroughly, one layer at a time. Measure exactly 2-1/2 cups prepared strawberries into 6- or 8-quart saucepot. Crush raspberries thoroughly, one layer at a time. Measure exactly 1-1/2 cups prepared raspberries into saucepot with strawberries. Crush blackberries thoroughly, one layer at a time. Measure exactly 1 cup prepared blackberries into saucepot with other fruit; mix well.
Stir pectin into fruit mixture in saucepot. Add butter to reduce foaming, if desired. Bring mixture to full rolling boil (a boil that doesn't stop bubbling when stirred) on high heat, stirring constantly. Stir in sugar. Return to full rolling boil and boil exactly 1 minute, stirring constantly. Remove from heat. Skim off any foam with metal spoon.
Ladle immediately into prepared jars, filling to within 1/4 inch of tops. Wipe jar rims and threads. Cover with 2-piece lids. Screw bands tightly. Place jars on elevated rack in canner. Lower rack into canner. (Water must cover jars by 1 to 2 inches. Add boiling water, if necessary.) Cover; bring water to gentle boil. Process 10 minutes. Remove jars and place upright on towel to cool completely. After jars cool, check seals by pressing middle of lid with finger. (If lid springs back, lid is not sealed and refrigeration is necessary.).