In this paper we investigate the phenomenon of multi-parent reproduction, i.e. we study recombination mechanisms where an arbitrary n>1 number of parents participate in creating children. In particular, we discuss scanning crossover that generalizes the standard uniform crossover and diagonal crossover that generalizes 1-point crossover, and study the effects of different number of parents on the GA behavior. We conduct experiments on tough function optimization problems and observe that by multi-parent operators the performance of GAs can be enhanced significantly. We also give a theoretical foundation by showing how these operators work on distributions.