This work concerns the comparison of supercritical water reactor (SCWR) assembly designs using coupled reactor physics and thermal-hydraulic methods. In the SCWR, large density gradients in the supercritical water (used as coolant and moderator) will require detailed multiphysics analysis. The Super Light Water Reactor (SLWR) was analyzed previously [Hughes et al., Nucl. Eng. Des., Vol. 270 (2014)], where MCNP5 was coupled with density and temperature results from a single-channel code. MCNP5 then provided the single-channel code with a linear heat profile. In the present work, that proposed assembly design is determined to have a negative density coefficient of reactivity. Two alternate designs with different geometries and water-to-fuel ratios are presently considered to address this issue. It is found that adding an additional row of pins is more effective at producing a positive density coefficient than is reducing the size of the moderator boxes.