  We investigate the effect of the quadratic correction $\alpha R^2$ and
non-minimal coupling $\xi \phi^2 R$ on a quintessence model with an exponential
potential $V(\phi) = M^4\exp(-\lambda\phi)$ in the Palatini formulation of
gravity. We use dynamical system techniques to analyze the attractor structure
of the model and uncover the possible trajectories of the system. We find that
the quadratic correction cannot play a role in the late time dynamics, except
for unacceptably large values of the parameter $\alpha$; although it can play a
role at early times. We find viable evolutions, from a matter-dominated phase
to an accelerated expansion phase, with the dynamics driven by the non-minimal
coupling. These evolutions correspond to trajectories where the field ends up
frozen, thus acting as a cosmological constant.
