In this work, based on the theory of electromagnetically induced transparency, optical bistability behavior in a diamond tin-vacancy color center system was theoretically investigated. It was found that a change in system parameters, such as the detuning of probe and coupled fields, intensities of the coupled fields, and cooperation parameters, can significantly change the quantum coherence characteristics of the system. This can be used to control the threshold of optical bistability of a solid system. In addition, the mutual transformation of optical bistability and optical multistability can be realized by properly adjusting the intensity of the coupled fields.