Combine greens, endive, radicchio, and lettuce in a large bowl; add avocado and haricot vert.
Remove peel and pith from grapefruit using a sharp paring knife. Working over a medium bowl to catch the juice, carefully cut between membranes to remove segments, and coarsely chop. Squeeze remaining membrane to extract juice; reserve.
To make the vinaigrette, whisk together reserved grapefruit juice, mustard, sugar, salt, and pepper in a medium bowl; add chopped grapefruit. While whisking constantly, add olive oil in a slow and steady stream until combined. Pour vinaigrette over salad and toss gently to coat. Transfer to a serving platter. Garnish with pomegranate seeds. Serve immediately.