Place potatoes in a 4-quart Dutch oven and add water to cover. Bring to boiling; reduce heat. Cover and simmer for 5 minutes. Add beans; return to boiling. Cover and simmer 5 minutes more or until potatoes and beans are just tender. Drain well.
Meanwhile, place 1/2 cup olives, oil, mustard, lemon juice, sugar, and pepper in a blender. Cover and blend until smooth.
To serve, place potato mixture and tuna on serving plates. Top with olive mixture. Garnish with lemon wedges, parsley, and additional olives, if desired.