Put the potatoes in a medium saucepan of salted water and bring to a boil. Boil for 5 minutes and then stir in the beans. Continue boiling until the beans and potatoes are tender, about 5 minutes longer. Drain thoroughly. When the potatoes are cool enough to handle, peel them and cut them into quarters.
Meanwhile, in a glass or stainless-steel bowl, whisk together the vinegar, mustard, salt, and pepper. Add the oil slowly, whisking. In a large glass or stainless-steel bowl, toss the romaine with 1/4 cup of the vinaigrette and then transfer to a platter or individual plates.
In the same bowl, toss the potatoes with 1 tablespoon of the vinaigrette and pile them on top of the romaine. Repeat with the green beans and the eggs, tossing each with 1 tablespoon of the vinaigrette and then arranging it on the romaine. Arrange the anchovies, capers, tuna, pimientos, and olives in piles on the lettuce. Pass any remaining vinaigrette at the table.