arbitrary number of “right-handed” neutrinos, either more or less than the number of left neutrinos. Here for illustration we first consider the minimalistic (3,1) model containing only one right-handed neutrino, in addition to the 3 known left-handed neutrinos. It has better stability properties than the fully sequential (3,3) seesaw mechanism which is then considered to further highlight the vacuum instability problem in pure type-I seesaw. We then show that vacuum stability can be improved by adding extra scalars as required, for example, in order to implement spontaneous violation of lepton number or to implement the scoto-seesaw mechanism [@Rojas:2018wym].

We analyse the scale at which instability sets in as a function of the magnitude of the Yukawa coupling relevant for generating neutrino mass in (3,1) as well as the conventional (3,3) seesaw schemes. We also study the role of extra scalars required in Majoron and scotogenic completions [@Rojas:2018wym] and study its improved stability properties.\
This work is organized as follows: In Section \[sec:sm-vac\] we revisit the vacuum stability problem in the [[Standard Model ]{}]{}showing that the Higgs quartic coupling becomes negative when RG-evolved to high scales. We then show in Section \[sec:seesaw\] that the vacuum stability problem becomes much worse in 