  We study a model including a real scalar field $\phi$ non-minimally coupled
to $F({\cal R})$ gravity, which is conformally equivalent to an
Einstein-Hilbert theory, involving two real scalar fields. We consider three
special cases of the potential of the field $\phi$ in the $F({\cal R})$-frame:
a vanishing potential, a mass term and a Higgs potential. All these lead to
non-trivial two-field potentials in the Einstein-frame which in particular
directions resemble the well-known Starobinsky model. We find, that all these
cases can yield viable inflationary models in complete agreement with current
observational data.
