In this work, we present a comprehensive extension of the Surface–Underground–Recharge (SUR) water supply model through the incorporation of generalized conformable derivatives. This operator enables the capture of more exotic dynamics within the system, enhancing the modeling framework’s ability to simulate complex hydrological interactions. Additionally, we extend the results to the restricted phase spaces of the analyzed dynamical systems, facilitating a deeper qualitative analysis. To achieve this, we augment the dimension of the generalized conformable SUR system, rendering it an autonomous higher-order system. Furthermore, we introduce a novel conformable function, referred to as the generalized linear conformable combination function, which significantly broadens the scope of our modeling capabilities. Thus, this study contributes to the advancement of hydrological modeling, providing a robust tool for analyzing intricate water resource dynamics in specific regions.