Peel the eggplant lengthwise, leaving 1-inch-wide strips of skin between each peeled section. Chop into 1 1/2-inch cubes.
In a large, heavy skillet, heat 1/4 cup EVOO over medium. Add the eggplant and cook until soft, stirring often and drizzling with more oil if too dry, 12 to 15 minutes. Stir in the marinara sauce and remove from heat.
In another large, heavy skillet, heat 1/4 cup EVOO over medium-high. Add the onion, celery, olives and capers and stir 1 minute. Add the white vinegar; bring to a simmer, then add the sugar and stir until dissolved, about 1 minute. Cook, stirring often, until the onions and celery are crisp-tender, 5 to 7 minutes. Add the onion-celery mixture to the skillet with the eggplant and fold gently to incorporate.
Transfer to a medium bowl, cover and refrigerate. Serve cold or at room temperature. Drizzle with EVOO before serving.