A multi-lobe approach was recently proposed to efficiently handle layered materials rendering [1]. To this end, the author introduces a low-order statistical representation for light-matter interactions and derives new adding equations for the framework. However, scattering volumes are poorly supported as the method does not account for back-scattering and resorts to single scattering approximations to avoid expensive doubling operations. In practice, this incurs severe energy losses yielding inconsistent dark appearances with increasing volume scattering (Fig. 1). Unfortunately, the adding equations introduced by the author can not be easily extended to handle both forward and backward propagating flux. We overcome these limitations with an efficient solution based on the transfer matrix. Under this formalism, each scattering component of the stack (scattering volume and interface) is described through a lightweight matrix, layering operations reduce to simple matrix products, and total flux accounting for multiple scattering are obtained thanks to matrix operators.