One of the most important characteristics of a Gaussian-to- uniform beam shaping system is the ratio of the entrance pupil radius to the spot size of the input Gaussian beam, i.e., its 1/e2 intensity radius. This parameter, called the beam shaping power, must be increased above a certain value, otherwise the homogeneity of the output beam decreases (due to Fresnel diffraction on the entrance pupil), and the power transmission of the optical system drops. We develop a new method for achieving a sufficiently large beam shaping power without the need for a special fabrication technology or design technique. The basic idea of our method is to place a number of low beam shaping power subsystems one after the other into a cascade, to obtain a system of increased beam shaping power. The subsystems can be constructed from simple elements (e.g., spherical lenses), which are easy to design and fabricate. We describe our method, develop simple formulas for its theoretical discussion, and present a design example to demonstrate its operation.