Tests of discrete symmetry violation have played an important role in understanding the structure of weak interactions in the Standard Model of particle physics. Historically, these measurements have been extensively performed in experiments with large samples of K and B mesons. A high luminosity τ -charm facility presents physicists with the opportunity to comprehensively explore discrete symmetry violation and test the Standard Model using τ leptons, charm mesons, and charmed baryons. This paper discusses several possible measurements for a future τ -charm factory.