  We show how to characterize the indistinguishability of up to four identical,
bosonic or fermionic particles, which are rendered partially distinguishable
through their internal degrees of freedom prepared in mixed states. This is
accomplished via their counting statistics when subjected to a highly symmetric
unitary acting upon their external (i.e., dynamical) degrees of freedom. For
pure internal states, we further extract information on the particles'
collective phases, which ultimately allows for an experimental reconstruction
of the full many-particle density operator up to complex conjugation.
