<p>In this study, we investigate the dynamical complexities of a predator–prey system with cooperative behavior of predators, fear and its carry-over effects, and additional food sources. To better reflect real-world scenarios, we expand the deterministic model into its stochastic counterpart by incorporating environmental white noise, impacting the mortality rates of both prey and predator species. The deterministic model exhibits a wealth of intricate dynamics, including various forms of bistability and tristability. We find that the cost of fear, enhancing intra-species competition among the prey, contributes to system stability. Additionally, we note that predator-induced fear, leading to the suppression of prey reproduction, exerts both stabilizing and destabilizing effects on the system’s dynamics. Furthermore, our results underscore the importance of minimal environmental disturbances in averting species extinction. Conversely, excessive environmental noise can drive both the species towards extinction. </p>