Can one ever prove that neutrinos are Dirac particles?

According to the “Black Box” theorem the experimental confirmation of neutrinoless double beta decay ($0\nu 2\beta$) would imply that at least one of the neutrinos is a Majorana particle. However, a null $0\nu 2\beta$ signal cannot decide the nature of neutrinos, as it can be suppressed even for Majorana neutrinos. In this letter we argue that if the null $0\nu 2\beta$ decay signal is accompanied by a $0\nu 4\beta$ quadruple beta decay signal, then at least one neutrino should be a Dirac particle. This argument holds irrespective of the underlying processes leading to such decays.