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We study solutions of the stellar structure equations for sphericallysymmetric objects in Palatini $f(R)=R+\alpha R^2$ and $f(R,Q)=R+\alphaR^2+\beta Q$ in the mass-radius region associated to neutron stars. Weillustrate the potential impact of the $R^2$ and $Q$ terms by studying a rangeof viable values of $\alpha$ and $\beta$. Similarly, we use different equationsof state (SLy, FPS, HS(DD2) and HS(TMA)) as a simple way to account for theequation of state uncertainty. Our results show that for certain combinationsof the $\alpha$ and $\beta$ parameters and equation of state, the effect ofmodifications of general relativity on the properties of stars is sizeable.Therefore, with increasing accuracy in the determination of the equation ofstate for neutron stars, astrophysical observations may serve as discriminatorsof modifications of General Relativity.

Neutron Stars in Palatini $R+\alpha R^2$ and $R+\alpha R^2+\beta Q$ Theories