  Holographic systems require monogamous mutual information for validity of
semiclassical geometry. This is encoded by the sign of the tripartite
information ($I3$). We investigate the behaviour of $I3$ for all partitionings
of systems in states which are highly entangled in a multipartite or bipartite
sense. In the case of multipartite entanglement we propose an algorithmic
construction that we conjecture can be used to build local maxima of $I3$ for
any partitioning. In case of bipartite entanglement we classify the possible
values of $I3$ for perfect states and investigate, in some examples, the effect
on its sign definiteness due to deformations of the states. Finally we comment
on the proposal of using $I3$ as a parameter of scrambling, arguing that in
general its average over qubits permutations could be a more sensible measure.
