  Following recent advancements, we consider a scenario of multipartite
postquantum steering and general no-signaling assemblages. We introduce the
notion of the edge of the set of no-signaling assemblages and we present its
characterization. Next, we use this concept to construct witnesses for
no-signaling assemblages without an LHS model. Finally, in the simplest
nontrivial case of steering with two untrusted subsystems, we discuss the
possibility of quantum realization of assemblages on the edge. In particular,
for three-qubit states, we obtain a no-go type result, which states that it is
impossible to produce assemblage on the edge using measurements described by
POVMs as long as the rank of a given state is greater than or equal to 3.
