Coat tuna steaks with 2 tablespoons olive oil and lemon juice and season with salt and pepper. Prepare grill or preheat broiler. Grill tuna, turning once, for about 6 minutes or until just cooked. Remove from grill and set aside.
Combine potatoes, beans, onions, capers, parsley, basil, remaining oil, vinegars, mustard, salt and pepper. Break the tuna into bite-size chunks and toss into potato mixture.
Line a large serving platter with red-leaf lettuce. Mound the tuna mixture in the center. Place tomatoes in a circle around the tuna salad. Garnish plate with quartered hard-boiled eggs, artichoke hearts, anchovies and Nicoise olives. Serve immediately. Serves 6 to 8.