We demonstrate that by dividing a Fresnel zone plate into a few regions having different periods in the s=r2 coordinate, then replacing the clear zones by a given distribution of pinholes, a so-called modified photon sieve is constructed. The first feature of the element is to increase its diameter without worrying about its feature size as the limiting factor in the fabrication zone plate. Moreover, it is shown that the number of the zones included in each region is an important parameter that has a great impact on handling the number of foci. So, by choosing a suitable relation between the number of the Fresnel zones of the regions, one gets a high-efficiency unifocal or bifocal or even multifocal element depending on the number of the regions and zones. This technique is detailed by making unifocal, bifocal, as well as trifocal modified photon sieves and surveying their focusing properties. Simulation studies are followed by the corresponding experiments to verify them.