  Charged lepton flavor violation arises in the Standard Model Effective Field
Theory at mass dimension six. The operators that induce neutrinoless muon and
tauon decays are among the best constrained and are sensitive to new-physics
scales up to $10^7\,$GeV. An entirely different class of
lepton-flavor-violating operators violates lepton flavors by two units rather
than one and does not lead to such clean signatures. Even the well-known case
of muonium--anti-muonium conversion that falls into this category is only
sensitive to two out of the three $\Delta L_\mu = - \Delta L_e = 2$
dimension-six operators. We derive constraints on many of these operators from
lepton flavor universality and show how to make further progress with future
searches at Belle II and future experiments such as $Z$ factories or muon
colliders.
