Fold a 36x18-inch piece of heavy foil in half to make an 18-inch square. Place pineapple in center of foil. Sprinkle with brown sugar and crystallized ginger. Bring up 2 opposite edges of foil; seal with a double fold. Fold remaining edges to completely enclose vegetables, leaving space for steam to build.
For a charcoal grill, place packet on the rack of an uncovered grill directly over medium coals about 10 minutes or until hot, turning occasionally. (For a gas grill, preheat grill. Reduce heat to medium. Place packet on a grill rack over heat. Cover and grill as above.)
Carefully open packet and transfer fruit mixture to serving bowl. Add berries. Sprinkle with demerara sugar. Makes 4 servings.