We theoretically investigate a nonlinear optical response of a planar microcavity with an embedded transition metal dicalcogenide monolayer when the energy of a biexcitonic transition is brought in resonance with the energy of a cavity mode. We demonstrate that the emission spectrum of this system strongly depends on an external pump. For small and moderate pumps, we reveal the presence of a doublet in the emission with the corresponding Rabi splitting scaling as a square root of the number of the excitations in the system. Further increase of the pump leads to the reshaping of the spectrum, which demonstrates, at weak damping, the pattern akin a Mollow triplet. An intermediate pumping regime shows a broad irregular spectrum reminiscent of a chaotic dynamics of the system.