  We write down a geometric realization of the Standard Model Effective Field
Theory (SMEFT) extended by $n_f$ flavours of light sterile neutrinos, a
so-called geo$\nu$SMEFT. As with the geoSMEFT introduced by Helset, Martin and
Trott, we show that a refactorization of the $\nu$SMEFT's operator product
expansion is possible, such that two- and three-point composite operator forms
are dressed with field-space connections composed of towers of Higgs dressings
and symmetry generators, valid at \emph{all-orders} in the
$\overline{v}_T/\Lambda$ expansion parameter of the EFT ($\overline{v}_T \equiv
\sqrt{2\langle H^\dagger H\rangle}$) . These connections are parameterized by
real Higgs coordinates and contribute to the field-space geometry of the
($\nu$)SM, with structure linked to the strength of Beyond-the-($\nu$)Standard
Model physics encoded in $\overline{v}_T/\Lambda$. In addition to enumerating
the relevant composite operators and associated connections, we briefly outline
the route to calculating all-$\overline{v}_T/\Lambda$-orders amplitudes,
including the flavor-invariant theory required to understand the neutrino
mass-eigenstate basis geometrically.
