Cut any large potatoes in half so they’re all a similar size and put them in the top of your steamer. Sprinkle with salt, cover and steam for 18 minutes. String the beans and slice them on the diagonal.
Drain the oil from the tuna into a bowl and whisk in the vinaigrette and mayo with salt and pepper to taste to make a creamy dressing.
Lift the top off the steamer and lower the eggs into the water beneath, making sure they are covered. Scatter the beans over the potatoes, return to the pan, cover and steam for 8 minutes more.
Lift off the potatoes and beans, then lift out the eggs and plunge them into cold water. Tip the potatoes and beans into the dressing and stir to coat. Shell and halve the eggs. Coarsely shred the lettuce into a large salad bowl, then tip the potatoes and beans on top, keeping back a couple of spoonfuls of dressing. Flake the tuna over the top, dot with the eggs and olives and drizzle over the reserved dressing.