We report the simultaneous increase of both nonlinear Kerr coefficient n2 and third-order nonlinear susceptibility χ^((3)) in aluminum zinc oxide (AZO) attained by pump-probe spectroscopy in a frequency degenerate configuration. Our experiments demonstrate a 6-fold enhancement in the third-order nonlinear susceptibility and over one order of magnitude increase in the nonlinear Kerr coefficient, while also determining two distinct operational wavelengths for optimal modulation of either the real or the imaginary part of the complex refractive index. These results, besides providing a broader spectral characterization of the third-order nonlinearity in AZO thin films, also show the fundamental advantages of performing nonlinear optics via degenerate excitation near the ENZ wavelength