  The Zee model for Dirac neutrinos is one of the simplest models featuring
one-loop Dirac neutrino masses. The interactions between the new scalars (two
singly-charged fields) and neutrinos induce general neutrino interactions (GNI)
which, as a generalisation of the non standard neutrino interactions,
constitute an additional tool to probe models beyond the SM like this. In this
work, we consider a $U(1)_{{B-L}}$ gauge symmetry as the responsible for the
Diracness of the neutrinos and the radiative character of the neutrino masses.
We determine the viable parameter space consistent with neutrino oscillation
data, leptonic rare decays and collider constraints, and establish the most
relevant experimental prospects regarding lepton flavor violation searches and
GNI in future solar neutrino experiments.
