Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.

Sift flour, baking powder, and baking soda into a medium bowl.

Mash sugar and margarine together in a separate bowl until creamy; beat in eggs until incorporated. Stir in flour mixture in 3 batches, alternating with mashed bananas, beating briefly after each addition, until smooth and well combined. Fold in plums. Transfer to the prepared baking dish.

Bake in the preheated oven until golden brown, about 1 hour.