In this paper, we present SCENE-Net V2, a new resource-efficient, \textbf{gray-box model} for multiclass 3D scene understanding. SCENE-Net V2 leverages Group Equivariant Non-Expansive Operators (GENEOs) to incorporate fundamental geometric priors as inductive biases, offering a more transparent alternative to the prevalent black-box models in the domain. This model addresses the limitations of its white-box predecessor, SCENE-Net, by expanding its applicability from pole-like structures to a wider range of datasets with detailed 3D elements.Our model achieves the sweet-spot between application and transparency: SCENE-Net V2 is a general method for object identification with interpretability guarantees.Our experimental results demonstrate that SCENE-Net V2 achieves competitive performance with a significantly lower parameter count. Furthermore, we propose the use of GENEO-based architectures as a feature extraction tool for black-box models, enabling an increase in performance by adding a minimal number of meaningful parameters.Our code is available in: https://github.com/dlavado/SCENE-Net-V2