  It is well-known that the Fundamental Identity (FI) implies that Nambu
brackets are decomposable, i.e., given by a determinantal formula. We find a
weaker alternative to the FI that allows for non-decomposable Nambu brackets,
but still yields a Darboux-like Theorem via a Nambu-type generalization of
Weinstein's splitting principle for Poisson manifolds.
