  Simple monomial inflationary scenarios have been ruled out by recent
observations. In this work we revisit the next simplest scenario, a
single--field model where the scalar potential is a polynomial of degree four
which features a concave ``almost'' saddle point. We focus on trans--Planckian
field values. We reparametrize the potential, which greatly simplifies the
procedure for finding acceptbale model parameters. This allows for the first
comprehensive scan of parameter space consistent with recent Planck and
BICEP/Keck 2018 measurements. Even for trans--Planckian field values the
tensor--to--scalar ratio $r$ can be as small as $\mathcal{O}(10^{-8})$, but the
model can also saturate the current upper bound. In contrast to the
small--field version of this model, radiative stability does not lead to strong
constraints on the parameters of the inflaton potential. For very large field
values the potential can be approximated by the quartic term; as well known,
this allows eternal inflation even for field energy well below the reduced
Planck mass $M_{\rm Pl}$, with Hubble parameter $H \sim 10^{-2} M_{\rm Pl}$.
More interestingly, we find a region of parameter space that even supports {\em
two phases of eternal inflation}. The second epoch only occurs if the slope at
the would--be saddle point is very small, and has $H \sim 10^{-5} M_{\rm Pl}$;
it can only be realized if $r \sim 10^{-2}$, within the sensitivity range of
next--generation CMB observations.
