We present a theoretical study of the nonlinear optical properties of shallow-donor impurities in semiconductors subjected to magnetic fields, hydrostatic pressures, and intense laser illumination within the Voigt configuration. The donor energy levels and their wave functions are obtained using a combination of nonperturbative and variational methods where intense laser field effects are exactly taken into account through a laser-dressed Coulomb potential (LdCP). The combined effects of radiation and magnetic fields, hydrostatic pressures, and temperatures on the linear, third-order nonlinear, and total optical absorption coefficients (OACs) for the 1s→2p± and 2pz transitions are investigated using a compact density-matrix approach. We find that the transition energies and geometric factors can be increased or decreased by changing external fields via the LdCP or by changing hydrostatic pressures and temperatures. In this way, saturable absorption depends not only on the incident optical intensity but also on the laser field, which is more easily realized in the z-polarization direction. The peak positions and magnitudes of the linear, third-order nonlinear, and total OACs can be effectively adjusted with an appropriate choice of these external perturbations. Moreover, hydrostatic pressures and temperatures affect these OACs in an opposite way. This opens a promising route to design new and efficient impurity-based devices manipulated by external perturbations.