  Entanglement is the resource to overcome the restriction of operations to
Local Operations assisted by Classical Communication (LOCC). The Maximally
Entangled Set (MES) of states is the minimal set of n-partite pure states with
the property that any truly n-partite entangled pure state can be obtained
deterministically via LOCC from some state in this set. Hence, this set
contains the most useful states for applications. In this work we characterize
the MES for generic three qutrit states. Moreover, we analyze which generic
three qutrit states are reachable (and convertible) under LOCC transformations.
To this end we study reachability via separable operations (SEP), a class of
operations that is strictly larger than LOCC. Interestingly, we identify a
family of pure states that can be obtained deterministically via SEP but not
via LOCC. To our knowledge these are the first examples of transformations
among pure states that can be implemented via SEP but not via LOCC.
