Rinse rabbit and pat dry; season all sides with salt and pepper. Heat 4 tablespoons oil in heavy large pot over medium-high heat. Add rabbit to pot and brown, turning often, (do not crowd, you may need to work in batches) about 8 minutes per batch. Transfer rabbit to bowl. Reduce heat to medium. Add remaining 2 tablespoons oil to pot. Add onion; sauté 5 minutes. Mix in potatoes, bell peppers, tomatoes, olives, celery, capers, garlic, and thyme; cook 5 minutes. Mix in wine, vinegar and 1/4 cup water. Add rabbit. Cover, reduce heat to medium-low and simmer 10 minutes. Cover and simmer until rabbit is tender, stirring occasionally and adding more water by 1/4 cupfuls if mixture is dry, about 30 minutes. Season with salt and pepper. Spoon vegetables into large dish. Top with rabbit. Garnish with parsley and serve warm.