  Characterising non-classical quantum phenomena is crucial not only from a
fundamental perspective, but also to better understand its capabilities for
information processing and communication tasks. In this work, we focus on
exploring the characterisation of Einstein-Podolsky-Rosen inference (a.k.a.
steering): a signature of non-classicality manifested when one or more parties
in a Bell scenario have their systems and measurements described by quantum
theory, rather than being treated as black boxes. We propose a way of
characterising common-cause assemblages from the correlations that arise when
the trusted party performs tomographically-complete measurements on their share
of the experiment, and discuss the advantages and challenges of this approach.
Within this framework, we show that so-called almost quantum assemblages
satisfy the principle of macroscopic noncontextuality, and demonstrate that a
subset of almost quantum correlations recover almost quantum assemblages in
this approach.
