Extension shapes are Maxwell plug-ins which provide their own geometry data to the renderer. There are two types of extension shapes:

Procedurals: the corresponding Maxwell extension implements its own ray intersection logic, so the render engine queries the object each time a ray is likely to hit it. Maxwell ships with a few extensions of this type, e.g. MaxwellHair, which renders procedural cones for hair follicles, and MaxwellParticles which renders analytic spheres at the location of the particles. When the MaxwellMayaExtensionShape object represents an extension of this type, the inherited GetShapeType method returns ShapeType_ProceduralExtension.
Loaders: the Maxwell extension creates triangle meshes when the engine processes the scene before rendering. This type of extension can be used to let the engine load geometry from 3rd party file formats at render time. An example would be the RFMeshes extension which can load RealFlow BIN mesh files. When the class wraps an object of this type, GetShapeType returns ShapeType_LoaderExtension.

To create an object of this type, call MaxwellMayaAPI::CreateExtensionShape with the required extension type and parameters.

This class doesn't add any new methods, it just implements those inherited from MaxwellMayaShape. All the parameters which need to be passed to the Maxwell extension are specified through the MaxwellMayaExtensionParams object which is given to MaxwellMayaAPI::CreateExtensionShape.

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