Step 1Place the tuna in a bowl and stir it with a wooden spoon to break it into large flakes. Stir in just enough of its oil to moisten it, 1 to 2 tablespoons. Add 1 tablespoon of the red onion and season to taste with salt.
Step 2Steam the potatoes until they are tender, about 20 minutes. As soon as the potatoes are cool enough to handle, slice them at least one-fourth-inch thick and place them in a mixing bowl. While the potatoes are still warm, season them with one-fourth teaspoon salt and a pinch of black pepper, about 2 tablespoons of the oil from the tuna and 1 teaspoon of vinegar. Gently stir in the capers and another tablespoon of red onion and arrange the seasoned potatoes in a low mound on a platter.
Step 3Steam the green beans until they are tender, about 6 minutes. Place them in the same mixing bowl and season with one-eighth teaspoon salt and a pinch of pepper, another tablespoon of red onion, the fresh olive oil and another teaspoon of vinegar. Scatter the green beans over the top of the potatoes on the platter.
Step 4If using salted anchovies, rinse them well to soften them and remove excess salt; if using oil-packed anchovies, slice each fillet lengthwise into 2 strips. Spoon the conserved tuna over the beans and garnish it with the remaining red onion, the pepper strips and the anchovy strips. Sprinkle with chopped parsley and serve immediately.