  Cosmological constraints on the sum of the neutrino masses can be relaxed if
the number density of active neutrinos is reduced compared to the standard
scenario, while at the same time keeping the effective number of neutrino
species $N_{\rm eff}\approx 3$ by introducing a new component of dark
radiation. We discuss a UV complete model to realise this idea, which
simultaneously provides neutrino masses via the seesaw mechanism. It is based
on a $U(1)$ symmetry in the dark sector, which can be either gauged or global.
In addition to heavy seesaw neutrinos, we need to introduce $\mathcal{O}(10)$
generations of massless sterile neutrinos providing the dark radiation. Then we
can accommodate active neutrino masses with $\sum m_\nu \sim 1$ eV, in the
sensitivity range of the KATRIN experiment. We discuss the phenomenology of the
model and identify the allowed parameter space. We argue that the gauged
version of the model is preferred, and in this case the typical energy scale of
the model is in the 10 MeV to few GeV range.
