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Coherent optical transmission systems can be modeled as a four-dimensional (4D) signal space resulting from the two polarization states, each with two quadratures. Recently, nonlinear analytical models have been proposed capable of capturing the impact of Kerr nonlinearity on 4D constellations. None of these addresses the inter-channel nonlinear interference (NLI) imposed by arbitrary modulation formats in multi-channel wavelength division multiplexed (WDM) systems. In this paper, we introduce a general nonlinear model for multi-channel WDM systems that is valid for arbitrary modulation formats, even asymmetric ones. The proposed model converges to the previous models, including the EGN model, in the special case of polarization multiplexed systems. The model focuses on the cross-phase modulation (XPM) nonlinear term that lies at the heart of the NLI in multi-channel WDM systems operating on standard high dispersion single-mode fiber. We show that strategic mappings of the modulation format's coordinates to the polarization states can reduce the NLI undergone by these formats.