We predict theoretically and demonstrate experimentally an ellipticity-dependent nonlinear magneto-optic rotation of elliptically-polarized light propagating in a coherent atomic medium. We show that this effect results from a hexadecapole and higher order momenta of atomic coherence, and is associated with an enhancement of Kerr and higher orders nonlinearities accompanied by suppression of the other linear and nonlinear susceptibility terms of the medium. These nonlinearities might be useful for quantum signal processing. In particular, we report an observation of an enhancement the polarization rotation of elliptically polarized light resonant with the 5S_{1/2} F=2 -> 5P_{1/2} F=1 transition of Rb87.
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