The system is pumped via a two-photon process. To achieve a population inversion, we engineer the quantum system and optimize its parameters, particularly the relaxation via an auxiliary low-Q cavity coupled to a transition between two excited states. We show numerically that such a maser can operate both in the intermediate coupling regime with super-Poissonian photon statistics and in the strong coupling regime, where the statistics is sub-Poissonian. For the former, the maser exhibits thresholdless behavior and for the latter, there is a well-defined pumping threshold. An interesting side-effect of the auxiliary resonator is that it allows overcoming the photon blockage effect for the pump, which would otherwise prohibit reaching high photon population. Finally, we observe the bistability of the steady-state Wigner function and the self-quenching effect for some parameters.