of a given measurement outcome [@acin2016certified], the maximum being achieved exactly by maximum entangled states. In practice, however, due to noise and other uncontrollable source of errors, we often might have weak or not maximum entanglement or nonlocal correlations [@PhysRevA.89.042106; @PhysRevA.86.012108]. To circumvent that, one has to rely on a distillation protocol: starting from two or more copies of a given resource, one can through a set of free operations extract a smaller number of copies but with more of the resource of interest. In the case of entanglement, these free operations are local operations and classical communication (since they cannot create or increase entanglement) [@RevModPhys.81.865]. In turn, the resource theory of nonlocality [@de_Vicente_2014] implies that such free operations are the so-called wirings [@PhysRevA.73.012101] (see Figure \[wiring\]).

The first nonlocality distillation protocol has been introduced in [@forster] and, since then, a number of results have been obtained [@brunner; @hoyer; @PhysRevLett.106.020402; @PhysRevA.80.062107; @Lang_2014; @PhysRevA.83.062114], for instance showing the existence of bound nonlocality [@PhysRevLett.106.020402] and the fact that post-quantum correlations with a negligible amount of nonlocality can make communication complexity trivial [@brunner]. In spite of that, it is fair to say that few general conclusions have been obtained, typically referring to very 