In a large pot or Dutch oven, heat the oil over medium heat. Add the squash, onions and bell peppers, and cook, stirring, until softened, about 5 minutes. Add the garlic and cook until fragrant, about 30 seconds. Add the curry paste and lime leaves, stir to combine, and cook for 1 minute. Add the fish sauce and sugar, and stir to combine. Add the coconut milk and bring to a boil. Lower the heat and simmer for 5 minutes. Add the mussels, cover, and cook, shaking the pan occasionally, until the mussels open, about 5 minutes. Discard any mussels that do not open. Stir in 1/4 cup of basil and remove from heat.

Allow to sit, covered, for 1 minute before serving. Discard any mussels that have not opened. Spoon into individual bowls or 1 large bowl. Garnish with the remaining 1/4 cup basil. Serve with rice and lime wedges.