  The processes with three or more charged particles in the final state exhibit
particular threshold behavior, as inferred by the famous Wannier law for (2e +
ion) system. We formulate a general solution which determines the threshold
behavior of the cross section for multiple fragmentation. Applications to
several systems of particular importance with three, four and five leptons
(electrons and positrons) in the field of charged core; and two pairs of
identical particles with opposite charges are presented. New threshold
exponents for these systems are predicted, while some previously suggested
threshold laws are revised.
