In a 4- to 5-quart pan over medium-high heat, stir onion in olive oil until soft and translucent, 3 to 5 minutes.

. Stir in corn, milk, coconut milk, water, and chili; bring to a simmer, reduce heat, and cook, stirring occasionally, until corn is tender to bite, 10 to 15 minutes.

With a slotted spoon, remove about 2 cups corn kernels from pan and reserve. In a blender or food processor, working in batches and holding down lid with a towel, whirl remaining corn mixture until smooth. Return to pan.

Add lime juice, basil, and reserved corn. Stir soup over medium heat until hot, 2 to 3 minutes. Add salt and pepper to taste. Ladle into bowls

Top with a spoonful of crab meat and a little extra basil, then garnish with lime wedges.