Mapping multiple materials to an OBJ model in THREE.js

Not the solution but a workaround: Why not converting your OBJ to glTF? Then you can use GLTFLoader, which has a built-in handling of DracoLoader.

Check out the following example: https://threejs.org/examples/#webgl_loader_gltf_extensions

Select the Duck model and then the Draco extension so see it in action.

Also see: A .glb model loaded using GLTFLoader isn't compressing despite using DRACOLoader