  We continue the development of axion monodromy inflation, focussing in
particular on the backreaction of complex structure moduli. In our setting, the
shift symmetry comes from a partial large complex structure limit of the
underlying type IIB orientifold or F-theory fourfold. The coefficient of the
inflaton term in the superpotential has to be tuned small to avoid conflict
with Kahler moduli stabilisation. To allow such a tuning, this coefficient
necessarily depends on further complex structure moduli. At large values of the
inflaton field, these moduli are then in danger of backreacting too strongly.
To avoid this, further tunings are necessary. In weakly coupled type IIB theory
at the orientifold point, implementing these tunings appears to be difficult if
not impossible. However, fourfolds or models with mobile D7-branes provide
enough structural freedom. We calculate the resulting inflaton potential and
study the feasibility of the overall tuning given the limited freedom of the
flux landscape. Our preliminary investigations suggest that, even imposing all
tuning conditions, the remaining choice of flux vacua can still be large enough
for such models to provide a promising path to large-field inflation in string
theory.
