Rinse, scrub, and debeard the mussels. Pat the shrimp and scallops dry with paper towels. For the Swiss chard, separate the leaves from the stems. Thinly slice the stems and roughly chop the leaves, keeping them separate.
If using lemongrass, trim the ends, remove the tough outer layers, and smash the pale inner stalk with the flat side of a knife. Slice it very thinly. Reserve some chopped green onions and cilantro for garnish.
Heat the oil in a large pot or Dutch oven over medium heat. Add the chard stems, most of the green onions, garlic, and lemongrass or kaffir lime leaves, if using. Cook for about 2 minutes until fragrant.
Stir in the red curry paste and cook for 1 minute. Pour in the stock, coconut milk, fish sauce, lime juice, and brown sugar. Stir until the sugar dissolves and bring to a gentle simmer.
Add the sliced carrots to the pot and cook for 2-3 minutes to slightly soften them.
Stir in the chard leaves. Arrange the mussels, shrimp, and scallops in the broth. Cover the pot and cook for 5 to 7 minutes.
The soup is done when the mussels have opened and the shrimp and scallops are opaque and cooked through. The internal temperature of the fish and seafood should reach 145°F (63°C).
Turn off the heat. Discard any mussels that did not open. Taste the broth and add a pinch of salt if needed.
Ladle the soup into bowls. Garnish with the reserved green onions, cilantro, and fresh basil before serving.