Four-photon stimulated Raman adiabatic passage–like (STIRAP-like) processes in the frame of the D1 optical transition line of atomic 39K are investigated theoretically by means of a rigorous model that takes into account all the atomic states involved in the interaction with the pump and Stokes light fields and is valid for any field intensities. The same sequential up-down-up-down transition involving two pump (up) and two Stokes (down) photons, going from the initial ground state |F=2,M=+2¿ to the final ground state |F=1,M=0¿, which was proven in the past to be very convenient for two-photon amplification and lasing, is considered here. The fact that two atomic states, one with F=1 and another with F=2, participate at each intermediate step of the multiphoton process makes the existence of an ideal unique adiabatic transfer state impossible, and at exact four-photon resonance the population-transfer efficiency to the final atomic state is low (below 60% in general, 80% in the best conditions). Nevertheless, it is shown that by choosing appropriate static detunings for the pump and Stokes fields with respect to the atomic transitions the system follows, sequentially, two adiabatic states, connected by an efficient diabatic passage, so that population-transfer efficiency asymptotically approaching 100% for increasing field amplitudes can be reached. These results are quite robust and suggest the possibility of using STIRAP (or STIRAP-like) pumping to, among other applications, increase the (presently very low) efficiency of two-photon amplification and lasing, a so far unfulfilled goal in quantum and nonlinear optics.