  Current experimental sensitivity on neutrino magnetic moments is many orders
of magnitude above the Standard Model prediction. A potential measurement of
next-generation experiments would therefore strongly request new physics beyond
the Standard Model. However, large neutrino magnetic moments generically tend
to induce large corrections to the neutrino masses and lead to fine-tuning. We
show that in a model where neutrino masses are proportional to neutrino
magnetic moments. We revisit, discuss and propose mechanisms that still provide
theoretical consistent explanations for a potential measurement of large
neutrino magnetic moments. We find only two viable mechanisms to realize large
transition magnetic moments for Majorana neutrinos only.
