high order non-linear processes is accomplished in the three-photon regime, when the transmon is coupled to weak bichromatic microwave fields with the same Rabi frequencies. A many-mode Floquet formalism, with longitudinal coupling, is used to simulate the quantum interferences in the absorption spectrum that manifest the multiphoton pumping processes in the transmon qubit. An intuitive graph theoretic approach is used to introduce to provide effective Hamiltonians that elucidate main features of the Floquet results. The analytical solutions also illustrate how controllability is achievable for desired single- or multiphoton pumping processes in a wide frequency range.