  The properties of collisionless shocks, like the density jump, are usually
derived from magnetohydrodynamics (MHD), where isotropic pressures are assumed.
Yet, in a collisionless plasma, an external magnetic field can sustain a stable
anisotropy. In \cite{BretJPP2018}, we devised a model for the kinetic history
of the plasma through the shock front, allowing to self-consistently compute
the downstream anisotropy, hence the density jump, in terms of the upstream
parameters. This model dealt with the case of a parallel shock, where the
magnetic field is normal to the front both in the upstream and the downstream.
Yet, MHD also allows for shock solutions, the so-called switch-on solutions,
where the field is normal to the front only in the upstream. This article
consists in applying our model to these switch-on shocks. While MHD offers only
1 switch-on solution within a limited range of Alfv\'{e}n Mach numbers, our
model offers 2 kinds of solutions within a slightly different range of
Alfv\'{e}n Mach numbers. These 2 solutions are most likely the outcome of the
intermediate and fast MHD shocks under our model. While the intermediate and
fast shocks merge in MHD for the parallel case, they do not within our model.
For simplicity, the formalism is restricted to non-relativistic shocks in pair
plasmas where the upstream is cold.
