The modified nonlinear wave dynamics due to band nonparabolicity and carrier heating, arising from parametrically interacting electron-longitudinal optical phonons in a polar semiconductor is studied both theoretically and numerically. Expressions for threshold pump required for the onset of polaron-induced parametric interaction and amplification characteristics are explicitly derived. Polaronic effects along with nonparabolicity are found to be additive and result in tremendous increment in the parametric gain. At smaller magnetic field and moderate carrier concentrations, nonlinearity in energy-dependent effective electron mass and collision frequency, affects threshold and amplification characteristics strongly, which can be utilized for the construction of optical switches.