In a 3- to 4-quart pan over high heat, bring 2 1/2 cups water and the rice to a boil; cover, reduce heat to low, and simmer until liquid is absorbed and rice is tender to bite, about 25 minutes.
Meanwhile, in a 10- to 12-inch frying pan over high heat, stir coconut milk, chicken broth, curry paste, fish sauce, and brown sugar until sugar and curry paste are dissolved and mixture is simmering. Stir in asparagus and clams, cover, and cook for 3 minutes. Add scallops and shrimp, cover, and cook, stirring occasionally, until clam shells have opened and shrimp and scallops are opaque but still moist-looking in the center (cut to test), about 3 minutes longer. Stir in lime juice.
Spoon rice into four wide, shallow bowls and top equally with seafood, asparagus, and sauce.