In large skillet heat 3 tablespoons of oil over medium heat.Add onions, celery, bell pepper and garlic, cover.
Cook until all vegetables are soft, about 5 to 7 minutes.

In a food processor, process chicken livers and andouille until smooth. Pour into skillet and cook. Stir occasionally until the meats are completely cooked - no red, about 10 minutes. Stir in the Cajun seasonings.
Set aside.

In a large Dutch oven, heat the remaining 2 tablespoons oil over medium heat. Add rice and cook, stirring almost constantly, until most of rice turns opaque, 2 to 3 minutes.
Stir  in the sausage mixture, stock, salt and pepper. Bring to boil over high heat.
Reduce heat to low and cover tightly. Cook until the rice is barely tender and has absorbed stock, about 15 to 20 minutes.

Remove from heat and let stand.
Stir well.

This can be used to stuff your turkey and then roast using your normal method.
Place any remaining dirty rice in a buttered baking dish. To reheat, drizzle with about 1/4 cup water or additional broth and bake in preheated oven at 350 F for 20 minutes.

Note: Louisiana is a leading rice-farming state so rice is a staple down here. A common recipe is based on "dirty" rice, colored brown by ground giblets and sausage mixture. While it may not be the prettiest dressing on the Bayou it sure is good with all the flavors supplied by meats, veggies, herbs and spices.