These files contain data supporting all results reported in J. Zheng, et al., Phonon-mediated third-harmonic generation in diamond. In J. Zheng, et al. we found: We observe strongly anisotropic third-harmonic generation mediated by resonant sum-frequency driving of Raman-active phonons with THz light, extending light-induced dual control of structural and optical properties in solids. Either strong enhancement or strong suppression of the third harmonic can be achieved, covering six orders of magnitude, a result of interference between purely electronic and phonon-mediated contributions to the polarization field. These findings enrich capabilities for tailoring nonlinear optics via phononics and for the spectroscopy of crystalline structural dynamics.