De Keyser and Roth recently have developed a kinetic model of the tangential discontinuity magnetopause. This model predicts (1) that not all configurations of magnetic field vectors and magnetosheath velocity allow an equilibrium to exist and (2) that there is a preference for a particular magnetic field rotation sense across the magnetopause due to the different response of ions and electrons to the electric field in the current layer. In the present paper we extend the original model to allow for different magnetospheric and magnetosheath densities and temperatures, and we show that the conclusions:remain essentially unchanged. Given the large-scale magnetosheath flow pattern around the magnetosphere, we also compute which regions of the dayside magnetopause may be in tangential discontinuity equilibrium for a given magnetosheath field orientation.