The deepest divide at the holiday table is not between Republicans and Democrats, but between Thanksgiving purists and progressives — those who insist on a hard-core traditional meal and those who flirt each year with different dishes.

It is possible for one cook to satisfy both camps, but it requires some ingenuity. Adding new ingredients to the old favorites is not the way; instead, add one or more new dishes to perennials on the table, and make sure they have modern, fresh flavors.

Some things should not be messed with. Glazing a turkey with pomegranate or rubbing it with chipotle won’t change anyone’s mind; people either like turkey or they don’t. Adding celery root, cheddar and the like to the classic mashed potatoes is risky. These days, plain, buttery, homemade mashed potatoes are a treat that everyone seems to look forward to at the holiday.

Beyond that, make sure there’s a creamed vegetable on the table — it doesn’t have to be onions — and a jellied cranberry sauce (canned is fine), so the reactionaries will be happy.

For the neophiles, your first move is adding a sprightly green vegetable, whether raw, roasted or blanched. A little salad of fresh herbs is very refreshing, but broccoli, string beans or spinach can also nestle in nicely on the table.

Next, prowl for recipes that include ingredients from different culinary traditions — Asian condiments, Moroccan spices, Middle Eastern syrups. These can add a welcome note of surprise to an all-too-familiar menu.

Soft Herb Salad

Adapted from “Ottolenghi: The Cookbook” by Yotam Ottolenghi and Sami Tamimi

Time: 1 hour

Yield: 6 to 8 servings (can be doubled)

Ingredients

FOR THE LOOSELY PACKED GREENS:

2 cups cilantro leaves

1 cup flat-leaf parsley leaves

1 cup small dill sprigs

1 cup basil or mint leaves

1 cup arugula leaves

2 cups purslane, mâche or hearts of Boston lettuce leaves

FOR THE DRESSING:

4 tablespoons unsalted butter

1 cup sliced almonds

Salt and coarsely ground black pepper

1/4 teaspoon red chili flakes or 1/2 teaspoon crushed pink peppercorns (optional)

3 tablespoons lemon juice, more to taste

2 tablespoons olive oil, more to taste

Preparation

1. Up to two days before serving, wash the herbs and greens: Fill a large bowl or clean sink with plenty of cold water. Immerse the leaves, swish around to loosen any dirt, then gently lift out. Dry in a salad spinner or by spreading them on clean kitchen towels. (When dry, refrigerate in sealed plastic bags or containers. Add a paper towel to each bag to absorb excess water.)

2. Melt butter in a frying pan until it sizzles. Add almonds. Sauté over low heat, until the almonds are golden and the butter is browned. Lift out almonds and drain on paper towels, reserving butter. (Butter can be kept for 1 day. Melt and cool again before assembling salad.)

3. When ready to serve, place greens in a large bowl. Add salt, pepper, chili flakes, almonds, cooking butter, lemon juice and olive oil. Toss gently and season to taste, then serve immediately.

Classic Mashed Potatoes

From Julia Moskin

Time: About 45 minutes

Yield: 4 to 6 servings

Ingredients

Salt

2 1/2 pounds potatoes (about 6 large potatoes), preferably a combination of russet (baking) potatoes and large Yukon Golds, or all Yukon Golds

4 tablespoons butter, more for dotting

1/3 cup whole milk

Preparation

1. In a large pot, bring a gallon of water and 2 tablespoons salt to a boil over high heat. Peel and quarter potatoes and keep in cold water until ready to cook. (This can be done up to 4 hours in advance.) Add potatoes to boiling water and boil about 15 to 20 minutes, until soft; a knife should go in with almost no resistance. (It is better to overcook than to undercook.)

2. In a saucepan or a microwave oven, heat butter and milk together until butter melts and mixture steams. Drain potatoes well and return to pot. Using an extruding masher or a ricer, mash hot potatoes until smooth. Lightly mix in about half of hot butter mixture, just until blended. Taste for salt and add more butter mixture until seasoned to your liking.

3. Stop here for fluffy potatoes. For creamy potatoes, keep stirring potato mixture, using a sturdy spoon to press it against sides and bottom of pot. Mix until dense and thick. For whipped potatoes, use a stand mixer to mash hot potatoes just until smooth, about 30 seconds. Add all the butter mixture and salt to taste, pulsing machine in short bursts at medium speed. When light and creamy, stop mixing immediately. (Potatoes can quickly become sticky.)

4. To keep hot until ready to serve, transfer to serving bowl, dot top with butter, cover tightly and keep in a warm place, like the back of the stove. Potatoes will stay hot for at least 30 minutes. To keep longer, place covered bowl in a pan holding about an inch of gently simmering water. Before serving, mix well.

Note: This recipe can be doubled, tripled and more.

Cranberry-Orange Jelly

Adapted from Canal House Cooking

Time: 20 minutes, plus at least 3 hours' chilling

Yield: 12 to 16 servings

Ingredients

1 1/2 cups Lillet (see note)

1/2 cup orange liqueur, like Grand Marnier

2 cups sugar

2 tablespoons juniper berries (optional)

2 12-ounce bags fresh or frozen cranberries (about 8 cups; frozen can be substituted)

Nonstick cooking spray (if chilling in a mold)

Preparation

1. In a heavy saucepan, combine Lillet, liqueur, sugar and juniper berries if using. Bring to a boil over medium-high heat. Add cranberries and return to a boil. Reduce the heat to low and simmer until all the cranberries burst and are very soft, at least 10 minutes total (or use a candy thermometer and cook mixture to 210 to 215 degrees). The mixture should be reduced and thickened, like a very loose jam.

2. Strain the sauce into a bowl through a sieve, pushing on the solids with a rubber spatula to extract all the liquid. Discard the solids. Stir the liquid and transfer to a pretty serving bowl or a mold. (If using a mold, spray the insides first with nonstick cooking spray.) A funnel or liquid measuring cup with a spout can be useful for transferring without splashing the sides. Cover and refrigerate for at least three hours, or up to several days. Keep refrigerated until ready to serve.

3. If you chilled the jelly in a mold, turn it out by placing the mold in a large bowl. Carefully pour hot water into the bowl so it comes up the sides of the mold, melting the jelly just enough to release it from the mold. After 3 minutes, try unmolding the jelly onto a serving dish. If it doesn’t come out, return to the bowl and try again 2 minutes later. Repeat until the jelly is released. If necessary, return it to the refrigerator to firm up before serving.

Note: Two cups of red wine, port, Madeira or orange juice can be substituted for the Lillet and the liqueur.