Previously [P.N.Hu, Phys. Fluids9, 89 (1966)], a universal monotonic profile was found for a weak plasma shock propagating perpendicular to a magnetic field using an elaborate set of moment equations which included electron and ion viscosity, coupled electron and ion heat conduction, thermal diffusion, and resistivity, together with distinct Hall terms for the resistivity, stress, and heat flow. Inclusion of an additional term related to electron inertia now gives a one‐parameter family of profiles which spans the entire range from collision dominated monotonic profiles to damped oscillatory profiles and the limiting collisionless case of purely oscillatory and solitary wave profiles.