Off-stoichiometry Heusler-like compounds provide a platform in which fractional site occupation can generate local orbital inequivalence beyond the conventional Slater-Pauling electron-counting picture. Here, we investigate the $\mathrm{XC}{\mathrm{o}}_{1.33}\mathrm{Z}$ family using first-principles density functional theory and dynamical mean-field theory (DMFT), and show that mixed 4c/4d occupation creates inequivalent Co-$e$ states with distinct orbital fillings, hybridization strengths, and correlation responses. The resulting 4c/4d inequivalence drives a short-range interplay between Co-$e$ states, establishing a local orbital configuration that underlies magnetic compensation. Crucially, our DMFT calculations reveal that this compensated state is not a simple uniform band-semiconducting ferrimagnet, but an orbital-differentiated correlated state characterized by a site-selective low-energy resonance on the ${\mathrm{Co}}^{4\mathrm{d}}\text{−}e$ orbital and a pseudogaplike spectral suppression on the ${\mathrm{Co}}^{4\mathrm{c}}\text{−}e$ orbital. High-throughput calculations across 27 $\mathrm{XC}{\mathrm{o}}_{1.33}\mathrm{Z}$ compositions further show that X-Z sublattice tunes the Co-$e$-orbital interplay, producing strong, moderate, and weak interplay regimes. The moderate-interplay regime provides the key window for compensated ferrimagnetism and potential orbital-differentiated correlated state. These results identify off-stoichiometry Heusler-like compounds as a tunable platform for realizing correlated electronic states coupled to macroscopic magnetic compensation.

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• Electronic structure
• Magnetism
• Density functional calculations
• Dynamical mean field theory
• Electron-correlation calculations
• First-principles calculations