Most intracavity MgO:LiNbO3 terahertz polariton lasers generate output in the 1–3 THz range. In this study, we investigate the potential to extend this tuning range toward 6 THz. We predict broader tuning using a modified polariton gain theory that takes account of additional polariton damping at 3.15 THz and the angle-dependent field overlap in the crystal.