Prepare pineapple ahead of serving time by peeling and coring and cutting the pulp into small wedges or cubes.
Add partly-thawed raspberries and sliced bananas at serving time. (I suggest thawing berries only partly because their flavor and texture is better if there are some ice crystals in them.)
Spoon ice cream into serving dishes.
Top with fruit mixture.
Pass sauce supreme to spoon over all.