We consider the behavior of optical bistability (OB) and multistability (OM) in a four-level atomic system involving a Rydberg state illuminated by a probe field as well as control and switching laser beams of larger intensity. When the switching field is absent, no OB arises because of the effect of Rydberg electromagnetically induced transparency. However, by application of the switching field, the hysteresis cycle appears to give rise to optical bistability, thanks to Rydberg electromagnetically induced absorption. It is further demonstrated that one can efficiently modify the OB threshold via suitable choices of system-controlling parameters. Interestingly, it is observed that this model can produce an optical switching between OB and OM with potential applications in logic-gate devices for optical communication.