Nonlinear phononics has recently been demonstrated as a viable approach for dynamically modifying materials' properties. Conventionally, nonlinearity in the lattice dynamics is introduced via the "ionic" Raman scattering, in which infrared-active phonons (i.e., coherent ionic vibrations) serve as the intermediate state for transferring energy to Raman-active phonons. Here we report that it is also possible to achieve phononic nonlinearity through the "electronic" route, a process that relies on excited electronic states to initiate energy exchange among Raman-active phonons. Taking layered ReSe2 as a model system, we use coherent phonon spectroscopy with a pump energy larger than the band gap to follow lattice dynamics and observe the nonlinear coupling between both Raman-active intralayer atomic oscillations and interlayer breathing modes. In addition, we show that such nonlinear phononic coupling is highly dependent on the environment temperature. This work, which demonstrates a different and novel mechanism, may enrich the toolkit for controlling material properties by means of nonlinear phononics.