Put the potatoes in a saucepan and cover with cold water. Bring to a boil and cook until tender, about 20 minutes. Drain and let cool, then thinly slice.
Meanwhile, put the green beans in a microwave-safe bowl and add a splash of water. Cover with plastic wrap and microwave until tender, 6 to 8 minutes. Drain and pat dry; set aside.
Make the dressing: Whisk the yogurt, vinegar and olive oil in a medium bowl; season with 1/4 teaspoon salt and a few grinds of pepper. Toss the romaine with 1 tablespoon of the dressing in a large bowl.
Divide the romaine among bowls. Arrange the red onion, green beans, salmon, olives, potatoes, tomatoes and white beans on top. Drizzle with the remaining dressing. Season with salt and pepper.