Sizable rates for charged lepton flavor violating processes are expected in many neutrino mass models. High scale models, such as the classical supersymmetric seesaw, typically predict that the 3-body decays $l_i to 3 l_j$ have rates roughly a factor $alpha$ smaller than those of the 2-body channel $l_i to l_j gamma$. We show that $Z^0$-penguin diagrams can give an enhancement for decays $l_i to 3 l_j$ in many extensions of the Minimal Supersymmetric Standard Model (MSSM), breaking the previous expectation. $mu-e$ conversion in nuclei gets also enhanced by the same type of diagrams, becoming a very constraining observable in many scenarios. We demonstrate this effect in two models, namely, the supersymmetric inverse seesaw and R-parity violating supersymmetry. Finally, two issues are briefly discussed: the presence of this effect in non-supersymmetric models and the non-decoupling behavior of the $Z^0$-penguins.