Supervised Neural Gas (SNG) introduces the margin-optimized cost function of Generalized Learn-ing Vector Quantization (GLVQ) equipped with neighborhood cooperation from Neural Gas (NG).This yields a highly interpretable learner that is less sensitive to the prototype initialization problem observed in the LVQ family of classification algorithms. Although Hammer, Strickert and Villmann presented the SNG framework as an extension applicable to any differentiable dissimilarity measure, the diagonal relevance weighting adaptation remains the only scheme to have been explored. In this paper, we investigate extensions of SNG with full matrix, local matrix, tangent and class-wise matrix distances by examining how rank-based cooperation interacts with metric parameterization learning. We provide gradient-level analysis of two failure modes: (I) gradient dilution and (II) subtraction amplification, which explain learning behavioral challenges in cooperation-based metric learning. We propose a Supervised Class-Wise Matrix Neural Gas variant (SCMNG) that identifies three structural conditions under which rank-based metric relevance learning can be achieved in light of these recorded failure modes. Ablation experiments against non-cooperative reference models indicate that the impact of rank-based cooperation depends on initialization quality, metric structureand class-wise conditions. When prototypes are placed in a representative manner, NG coopera-tion mainly results in gradient interference. In contrast, with poor initialization, NG cooperationfacilitates the distribution of prototypes across class regions.