In a past version, maybe .72, you could cast and receive shadows with the MeshBasicMaterial. It was simple. Then the concept of ambient light changed in three.js and MeshBasicMaterial could no longer support shadows.
THREE.ShadowMaterial was introduced to compensate for the limitation. It works great! But it really only works on PlaneGeometry because by it's nature, THREE.ShadowMaterial is transparent, so the shadows cast inside and outside the object3d with ShadowMaterial are seen.
The idea is that you use two meshes, one with the MeshBasicMaterial, and the other with ShadowMaterial.
shape = new THREE.BoxGeometry(1,1,1),
basicMaterial = new THREE.MeshBasicMaterial({
color: 0xff0000
}),
mesh = new THREE.Mesh(shape, basicMaterial),
shadowMaterial = new THREE.ShadowMaterial({opacity:.2}),
mesh2 = new THREE.Mesh(shape, shadowMaterial),
You can see an example of the problem, here: https://jsfiddle.net/7d47oLkh/
The shadows cast at the bottom of the box are incorrect for the use-case.
The answer is, NO. There is no easy way to support full-bright basic materials that also accept and cast a shadow in three.js.