A strategy for designing optical systems that are optimized for multiple optical functions on the basis of wave optics is presented. Each optical function is composed of an input field, a set of fixed system parameters, and a merit function. A design algorithm is proposed that is applicable for optical systems consisting of a transmission operator followed by an arbitrary linear operator. The goal is to find the transmission operator, which is optimal for all optical functions simultaneously. In later design steps, this transmission operator can be transformed to real optical elements, for instance, by using the thin element approximation. It is shown that the algorithm is efficiently applicable by investigating two sample applications for multifunctional wave optical design: the design of tolerant systems and 3-D beam shaping.