Here are popular burger chains (mostly U.S.) known for letting you customize toppings — short notes on how they work so you can pick the style you want:

• Five Guys — fully customizable free toppings (lettuce, tomato, grilled onions, mushrooms, jalapeños, etc.) and lots of free sauces; you can add extra patties/cheese for a price.
• Shake Shack — build or modify Shack burgers; offers standard and seasonal toppings plus add-ons (bacon, cheese, fried eggs, pickles, ShackSauce).
• Smashburger — choose from preset burgers or build-your-own with many toppings and spreads; offers different buns and cheeses.
• Red Robin — casual-dining chain with extensive build-your-own options and a long list of toppings, sauces, and premium add-ons; also offers Bottomless Fries.
• Fuddruckers — “build your own” at the counter with many cheeses, fresh veggies, and specialty sauces; known for large patties and buns.
• Bareburger — focus on organic/alternative proteins (beef, bison, plant-based) with many toppings and bun/cheese options.
• BurgerFi — customizable burgers with premium toppings, plant-based patties, and add-ons like onion straws and different cheeses.
• The Habit Burger Grill — customizable toppings and add-ons; also chargrilled flavor options.
• In-N-Out — simpler menu but highly customizable (add Animal Style, extra patties/cheese, grilled onions, hold items, etc.).
• Carl’s Jr. / Hardee’s — broad build-your-own choices and premium add-ons; often run limited-time specialty toppings.
• Steak ‘n Shake — order customizable burgers with a variety of toppings and shakes on the side.
• HopDoddy — craft burgers with mix-and-match options and premium toppings (bacon jam, fancy cheeses, house sauces).
• Smash / fast-casual local concepts and many regional chains (e.g., Wahlburgers, Umami Burger) — typically offer custom toppings or mix-and-match menus.

Quick tips:

• If you want full freedom to build, look for fast-casual places that advertise “build your own” (Five Guys, Smashburger, Fuddruckers, Bareburger).
• For premium/creative toppings (artisanal cheeses, house condiments), try gastropub-style chains (HopDoddy, Umami, Red Robin).
• If you want plant-based options + customization, check Bareburger, BurgerFi, and many chains now offer plant-based patties.

If you want a list filtered by city, price range, or strictly fast-food vs. sit-down, tell me the city or preferences and I’ll narrow it down.