  A possible explanation for the discrepancy between electronic and muonic
hydrogen measurements of the proton charge radius are new, lepton-universality
violating interactions. Several new couplings and particles have been suggested
that account for this discrepancy. At present, these explanations are poorly
constrained. Experiments such as the upcoming kaon decay experiment at JPARC
may constrain or eliminate some explanations by sensitivity to the decay
channel $K^+ \rightarrow \mu^+ +\nu + e^- + e^+$. We calculate the predicted
contributions of the various explanations to this channel. The predicted
signals, if present, should be large enough to be resolved in the experiment.
