The steady-state optical bistability (OB) and optical multistability (OM) behavior in the quasi-Λ-type atomic system driven by a probe field and a coherent coupling field inside a unidirectional ring cavity are shown, and the effects of coupling-field detuning and coupling-field intensity on the OB and OM behavior are investigated. The transition from OB to OM or vice versa is found by varying the detuning of the coherent coupling field or by adjusting the intensity of the coupling field. The influence of the atomic cooperation parameter on the OM behavior is also discussed.