  Which nonlocal correlations can be obtained, when a party has access to more
than one subsystem? While traditionally nonlocality deals with spacelike
separated parties, this question becomes important with quantum technologies
that connect devices by means of small shared systems. Here we study Bell
inequalities where measurements of different parties can have overlap. This
allows to accommodate problems in quantum information such as the existence of
quantum error correction codes in the framework of non-locality. The scenarios
considered show an interesting behaviour with respect to Hilbert space
dimension, overlap, and symmetry.
