Roll out dough to an 18-inch round on lightly floured parchment (parchment should measure at least 18 inches square; overlap 2 pieces, if necessary).
Combine plums, lemon juice, flour, salt, and 3/4 cup granulated sugar. Gently stir in blackberries and place in middle of pastry, leaving a 3-inch border. Dot top of fruit mixture with butter. Fold up edges of pastry to partially cover fruit; brush pastry with egg wash and sprinkle with sanding sugar. Slide galette on parchment onto a rimmed baking sheet (trim parchment to fit, if necessary). Refrigerate until dough is firm, about 30 minutes.
Meanwhile, preheat oven to 425 degrees. Bake galette 30 minutes. Reduce heat to 375 degrees and bake until pastry is golden and juices are bubbling, about 30 minutes more. Let cool completely on a wire rack, about 2 hours.
Stir together yogurt and remaining tablespoon granulated sugar. Cut galette into wedges and serve with sweetened yogurt.