A topping is not the same job in every register. In a Cincinnati parlor it is the dish. In an ICS Traditional Red cup it is a disqualification. In a Texas high-school stadium it is the bag. Read the service as cookery.
Cincinnati: the ways are the plate
Serious Eats’ serving note: a two-way is spaghetti and chili; a three-way, “Cincinnati chili’s most classic form,” is spaghetti, chili, and cheese; a four-way adds diced sweet onions or canned kidney beans; a five-way gets both. WVXU lists the same ladder and adds that a one-way (just chili) is not how people order. Atlas Obscura: parlors put chili on spaghetti; you get oyster crackers; there is no side of cornbread; a mild hot sauce sits on the table; locals cut each bite with the side of the fork instead of twirling.
The cheddar is not a sprinkle. It is a heap. The spaghetti is not a bed you could swap for rice without leaving the style. Coneys, chili on a hot dog with mustard, onion, and cheese, are the other Cincinnati service, named on the same pages. Beans in a five-way are on the dish, not in the pot.
Texas: Fritos, saltines, onion, cheese
Texas Highways puts the state dish on white tablecloths and “in a Styrofoam cup mixed with Fritos at a football game.” Eater’s Frito pie explainer: not pie; Fritos with chili on top, often in the bag; in Texas typically garnished with shredded cheddar and chopped raw onion. Optional extras (queso, pickled jalapeño, sour cream) exist; “purists would surely frown.” Robb Walsh, quoted there, ties the popularity to Texas high-school concession stands: tear the bag, ladle the condiment-holder options.
The New York Times, on Super Bowl Tex-Mex, repeats the bag version (“walking tacos”) and the origin fight (Daisy Doolin versus a Santa Fe Woolworth’s versus a 1949 Texas cookbook). Southern Living’s Texas plate note: chili con carne “commonly comes served with corn bread, saltine crackers, or corn chips with a sprinkle of cheese and diced onion.”
López-Alt’s Texas method lists table options, not requirements: cilantro, chopped onions, scallions, grated cheese, avocado, warm tortillas. That is home service on a no-beans pot. It is not an ICS cup.
Worked example. Same onion, three jobs
Raw diced onion on a Frito pie is a Texas concession topping (Eater, NYT). Raw onion on a Cincinnati four-way is a named way (Serious Eats). Onion cooked into a CASI pot is legal if the dice is even and mixed through (CASI rules). Onion sitting on top of an ICS Traditional Red judging cup is a garnish and a DQ (ICS PDF). The allium did not change. The register did.
Oklahoma: spaghetti and coneys, without pretending to be Cincinnati
The Oklahoma Historical Society entry is specific: Ike’s in Tulsa served chili alone, with beans, on spaghetti, or with beans on spaghetti. Christ Economou’s Coney Island in Tulsa (1926) served hot dogs with mustard, onions, or chili, no beans; the chili included cinnamon, chili powder, red pepper, and paprika. Oklahoma City’s Soter Coney Island later specialized in Greek-style chili on spaghetti and hot dogs. The state ate Texas red and Midwest parlor service at once. That is documented foodways, not a claim that Tulsa invented the three-way.
Rice, crackers, lime, cilantro
Rice under chili is common home and cafeteria service; it is a filler if it goes in the contest pot (ICS Traditional Red and CASI both forbid rice in the chili). Oyster crackers belong to Cincinnati parlor tables (Atlas Obscura, WVXU’s serving culture). Saltines belong to the Southern Living Texas list. Lime and cilantro show up on Kenji’s table list and on a lot of home chile-verde bowls; they are not Cincinnati parlor kit, and they are not an ICS garnish.
Cheese: bright yellow shredded cheddar is Cincinnati’s three-way. Cheddar on Frito pie is Texas concession. A CASI cup does not get a melt on top.
What the public pages already named
Onion, cheese, Fritos, spaghetti, and saltines belong to the pots that already claimed them in public. A Florida cook-off that sets crackers on the tasting table is event logistics, not a new regional topping.
A thin Cincinnati sauce wants a tall pot more than a reducing Dutch oven. A Frito-pie chili can come from either. Dutch oven vs stockpot.
Leftover chili poured over Fritos is still leftover meat stew. USDA USDA: refrigerate within two hours; 3 to 4 days in the fridge; reheat leftovers to 165 °F; bring soups, sauces, and gravies to a rolling boil. The 2-hour clock is 1 hour if the air is above 90 °F. A cook-off tasting table in August is that case. The bag, the saltines, and the spaghetti do not pause it.