It　is　well　known　that　in　the　quantum　Rabi　model,　a　three-photon　resonance　occurs　when　the　cavity　field　bare　frequency　is　about　1/3　of　the　atomic　transition　frequency.　In　this　manuscript,　we　show　that　the　resonance　can　also　be　generated　in　the　absence　of　the　＂1/3　condition＂by　employing　an　artificial　atom　with　tunable　transition　frequency.　To　realize　the　protocol,　the　modulation　frequency　should　be　comparable　to　the　cavity　frequency　in　order　to　induce　a　counter-rotating　interaction　in　the　effective　Hamiltonian.　In　this　way,　three-photon　Rabi　oscillations　can　be　observed　in　a　small-detuning　regime,　avoiding　the　excitation　of　high-energy　states　of　the　atom.　We　derive　an　effective　Hamiltonian　(equivalent　to　the　anisotropic　Rabi　model　Hamiltonian)　to　determine　the　magnitude　of　the　energy　splitting　and　the　resonance　position.　Numerical　simulation　results　show　that　the　protocol　not　only　generates　a　three-photon　resonance,　but　also　has　a　detectable　output　photon　flux.　We　hope　the　protocol　can　be　exploited　for　the　realization　of　Fock-state　sources　and　the　generation　of　multiparticle　entanglement.　　©　2024　American　Physical　Society.