In this study, we investigate the optical bistability (OB) and optical multistability (OM) phenomena within a V-type three-level atomic system interacting with two independent broadband squeezed baths confined in a unidirectional cavity. Our analysis reveals that the transition between OB and OM is influenced by the strength of the control field and the intensity of the squeezed vacuum. Notably, the impact of each of these factors on the transition exhibits distinct characteristics. Furthermore, we explore the effects of additional system parameters, such as the incoherent pumping rate and cooperation parameter. Our findings emphasize the crucial roles played by these parameters in shaping the observed results. Specifically, we observe that variations in the incoherent pumping rate and cooperation parameter contribute significantly to the system’s OB and OM behavior, further underscoring the multifaceted nature of the studied atomic system. This comprehensive investigation not only elucidates the intricate interplay between key parameters but also unveils the sensitivity of the system to variations in control field strength, intensity of the squeezed vacuum, incoherent pumping rate, and cooperation parameter.