  We study an extension of the Standard Model with electroweak scale
right-handed singlet fermions $N$ that induces neutrino masses, plus a generic
new physics sector at a higher scale $\Lambda$. The latter is parametrized in
terms of effective operators in the language of the $\nu$SMEFT. We study its
phenomenology considering operators up to $d=6$, where additional production
and decay modes for $N$ are present in addition to those arising from the
mixing with the active neutrinos. We focus on the production with four-Fermi
operators and we identify the most relevant additional decay modes to be $N\to
\nu \gamma$ and $N\to 3f$. We assess the sensitivity of future Higgs factories
on the $\nu$SMEFT in regions of the parameter space where the new states decay
promptly, displaced or are stable on detector lengths. We show that new physics
scale up to $5-60\;$TeV can be explored, depending on the collider considered.
