We present a theoretical study of the interaction between light and a cold gas of three-level, ladder configuration atoms close to two-photon resonance. In particular, we investigate the existence of collective atomic recoil lasing (CARL) instabilities in different regimes of internal atomic excitation and compare to previous studies of the CARL instability involving two-level atoms. In the case of two-level atoms, the CARL instability is quenched at high pump rates with significant atomic excitation by saturation of the (one-photon) coherence, which produces the optical forces responsible for the instability and rapid heating due to high spontaneous emission rates. We show that in the two-photon CARL scheme studied here involving three-level atoms, CARL instabilities can survive at high pump rates when the atoms have significant excitation, due to the contributions to the optical forces from multiple coherences and the reduction of spontaneous emission due to transitions between the populated states being dipole forbidden. This two-photon CARL scheme may form the basis of methods to increase the effective nonlinear optical response of cold atomic gases.