We investigate the capacity region of multi-user interference channels (IC), where each user encodes multiple sub-user components. By unifying chain-rule decomposition with the Entropy Power Inequality (EPI), we reason that single-user Gaussian codebooks suffice to achieve optimal performance, thus obviating any need for intricate auxiliary variables or joint typicality arguments. Our partial-MAC formulation enumerates sub-user decoding orders while only imposing constraints for sub-users actually decoded. This significantly reduces complexity relative to enumerating all subsets or bruteforcing over all successive interference cancellation (SIC) decoding order combinations at all receivers. This leads to a finite but comprehensive construction of all achievable rate tuples under sum-power constraints, while guaranteeing that each receiver fully recovers its intended sub-user signals. Consequently, known single-user Gaussian capacity results generalize naturally to multi-user scenarios, revealing a cohesive framework for analyzing multi-user IC. Our results thus offer a streamlined, tractable pathway for designing next-generation cell-free wireless networks that rely on IC mechanisms, efficiently exploiting interference structure while minimizing overhead. Overall, this provides a unifying perspective.