  Generalized Einstein - Aether vector field models have been shown to provide,
in the weak field regime, modifications to gravity which can be reconciled with
the successfull MOND proposal. Very little is known, however, on the function
F(K) defining the vector field Lagrangian so that an analysis of the viability
of such theories at the cosmological scales has never been performed. As a
first step along this route, we rely on the relation between F(K) and the MOND
interpolating function $\mu(a/a_0)$ to assign the vector field Lagrangian thus
obtaining what we refer to as "MONDian vector models". Since they are able by
construction to recover the MOND successes on galaxy scales, we investigate
whether they can also drive the observed accelerated expansion by fitting the
models to the Type Ia Supernovae data. Should be this the case, we have a
unified framework where both dark energy and dark matter can be seen as
different manifestations of a single vector field. It turns out that both
MONDian vector models are able to well fit the low redshift data on Type Ia
Supernovae, while some tension could be present in the high z regime.
