  We present a method that allows the study of classical and quantum
correlations in networks with causally-independent parties, such as the
scenario underlying entanglement swapping. By imposing relaxations of
factorization constraints in a form compatible with semidefinite programming,
it enables the use of the Navascu\'es-Pironio-Ac\'in hierarchy in complex
quantum networks. We first show how the technique successfully identifies
correlations not attainable in the entanglement-swapping scenario. Then we use
it to show how the nonlocal power of measurements can be activated in a
network: there exist measuring devices that, despite being unable to generate
nonlocal correlations in the standard Bell scenario, provide a
classical-quantum separation in an entanglement swapping configuration.
