  Quantum steering is the phenomenon whereby one party (Alice) proves
entanglement by "steering'' the system of another party (Bob) into distinct
ensembles of states, by performing different measurements on her subsystem.
Here, we investigate steering in a network scenario involving $n$ parties, who
each perform local measurements on part of a global quantum state, that is
produced using only two-party entangled states, and mixing with ancillary
separable states. We introduce three scenarios which can be straightforwardly
implemented in standard quantum optics architecture, which we call random
$\frac{n}{2}$-pair entanglement, random pair entanglement and semi-random pair
entanglement. We study steerability of the states across two-party marginals
which arise in the three scenarios, and derive analytically the necessary and
sufficient steering criteria for different sets of measurement settings.
Strikingly, using the semi-random pair entanglement construction, one party can
steer every one of the $n-1$ other parties, for arbitrarily large $n$, using
only two measurements. Finally, exploiting symmetry, we study various small
network configurations (three or four parties) in the three scenarios, under
different measurements and produced by different two-party entangled states.
