Crystal plasticity models establish connections between macroscopic observations and microscopic plasticity mechanisms. However, the scale disparity between observables and underlying plasticity mechanisms complicates the estimation of certain material parameters, particularly slip system interaction coefficients. To bridge the gap between observations and plastic deformation mechanisms, Berkovich nanoindentation residual topographies can be used as observables for identifying crystal plasticity parameters. This study focuses on simultaneously identifying slip system interaction coefficients through an inverse approach using Berkovich nanoindentation topographies. We first establish an experimental database of residual topographies. Then, guided by a local a priori identifiability analysis, we select optimal experiments to identify all work-hardening parameters. The parametric identification employs the finite element model updating (FEMU) method, followed by a posteriori validation to assess solution stability and experimental-numerical correspondence. The results reveal a distinct hierarchy of interaction coefficients, characterized by stronger sessile and weaker glissile interactions.