  It has been recently shown, that some of the tripartite boxes admitting
bilocal decomposition, lead to non-locality under wiring operation applied to
two of the subsystems [R. Gallego et al. Physical Review Letters 109, 070401
(2012)]. In the following, we study this phenomenon quantitatively. Basing on
the known classes of boxes closed under wirings, we introduced multipartite
monotones which are counterparts of bipartite ones - the non-locality cost and
robustness of non-locality. We then provide analytical lower bounds on both the
monotones in terms of the Maximal Non-locality which can be obtained by Wirings
(MWN). We prove also upper bounds for the MWN of a given box, based on the
weight of boxes signaling in a particular direction, that appear in its bilocal
decomposition. We study different classes of partially local boxes and find MWN
for each class, using Linear Programming. We identify also the wirings which
lead to MWN and exhibit that some of them can serve as a witness of certain
classes. We conclude with example of partially local boxes being analogue of
quantum states that allow to distribute entanglement in separable manner.
