Integration of multiple geophysical methods in combined data analysis is a key practice to reduce model uncertainties and enhance geological interpretations. Electrical resistivity models resulting from inversion of marine magnetotelluric (MT) data, often lack depth resolution of lithological boundaries, and distinct information for shallow model parts. This is due to the nature of the physics i.e. diffusive method, model regularization during inversion, and survey setup i.e. large station spacing and missing high frequency data. Thus, integrating data or models to constrain layer thicknesses or structural boundaries is an effective approach to derive better constrained, more detailed resistivity models. We investigate the different impacts of three cross-gradient coupled constraints on 3D MT inversion of data from the Namibian passive continental margin. The three constraints are a) coupling with a fixed structural density model; b) coupling with satellite gravity data; c) coupling with a fixed gradient velocity model. Here we show that coupling with a fixed model (a and c) improves the resistivity model most. Shallow conductors imaging sediment cover are confined to a thinner layer in the resulting resistivity models compared to the MT-only model. Additionally these constraints help to suppress vertical smearing of a conductive anomaly attributed to a fracture zone, and clearly show that the seismically imaged Moho is not accompanied by a change in electrical resistivity. All of these observations aid interpretation of an Earth model indicating involvement of a plume impact in continental break-up during the early Cretaceous.