  We present the first instance where post-quantum steering is a
stronger-than-quantum resource for information processing -- remote state
preparation. In addition, we show that the phenomenon of post-quantum steering
is not just a mere mathematical curiosity allowed by the no-signalling
principle, but it may arise within compositional theories beyond quantum
theory, hence making its study fundamentally relevant. We show these results by
formulating a new compositional general probabilistic theory -- which we call
Witworld -- with strong post-quantum features, which proves to be a intuitive
and useful tool for exploring steering and its applications beyond the quantum
realm.
