  We study an artificial spin ice system consisting of two identical layers
separated by a height offset $h$. For small separation, the layers are shown to
attract each other, provided the whole system is in the ground state. Such an
attraction comes about by means of a power-law force that we compare to van der
Waals forces. When magnetic monopoles occur in one (or both) layers, the
scenario becomes even more interesting and these layers may also repel each
other. By tuning parameters like $h$ and monopole distance, switching between
attraction and repulsion may be accomplished in a feasible way. Regarding its
thermodynamics, the specific heat peak shifts to lower temperature as $h$
increases.
