  We extend the Coleman--Weinberg inflationary model where a scalar field
$\phi$ is non-minimally coupled to gravity with the addition of the $R^2$ term.
We express the theory in terms of two scalar fields and going to the Einstein
frame we employ the Gildener--Weinberg formalism, compute the one-loop
effective potential and essentially reduce the problem to the case of
single-field inflation. It turns out that there is only one free parameter,
namely, the mixing angle between the scalars. For a wide range of this angle,
we compute the inflationary observables which are in agreement with the latest
experimental bounds. The effect of the $R^2$ term is that it lowers the value
of the tensor-to-scalar ratio $r$.
