Whisk together olive oil, red wine vinegar, minced shallot, Dijon mustard, salt and pepper.
Bring a medium-size pot of salted water to a boil. Add new potatoes to boiling water for 6 minutes; drain and run under cool water.
Place baby spinach in a large serving bowl with potatoes, plum tomatoes, green beans, black olives and 3 cans (5 oz) albacore tuna. Drizzle with dressing; toss well to coat. Place salad mixture on serving platter and crumble 1 additional can of albacore tuna, drained, over top. Add hard-cooked eggs, peeled and cut into wedges, and serve immediately