In a 3- to 4-quart pan over high heat, combine coconut milk, rice, and 3/4 cup water. Bring to a boil, reduce heat, cover, and simmer until rice is tender to bite, about 15 minutes.
Meanwhile, cut peel and membrane from grapefruit. Cut between fruit and membrane to release segments into a bowl.
In a 10- to 12-inch frying pan, mix sugar and cornstarch. Add soy sauce, vinegar, and ginger. Stir on high heat until boiling, about 1 minute. Add shrimp and stir often until opaque but still moist-looking in center of thickest part (cut to test), 3 to 4 minutes.
Mound rice equally on warm plates, spoon shrimp mixture equally onto rice, and garnish with grapefruit segments, endive leaves, and basil.