In designing a state space of possible designs is implied by the representation used and the computational processes that operate on that representation. GAs are a means of effectively searching that state space which is defined by the length of the genotype's bit string. Of particular interest in design computing are processes that enlarge that state space to change the set of possible designs. This paper presents one such process based on the generalization of the genetic crossover operation. A crossover operation of genetic algorithms is reinterpreted as a random sampling of interpolating phenotypes, produced by a particular case of phenotypic interpolation. Its generalization is constructed by using a more general version of interpolation and/or by adding extrapolation to interpolation. This generalized crossover has a potential to move the current population outside of the original state space. An adaptive strategy for state space enlargement, which is based on this generalization, is designed. This strategy can be used for computational support of creative designing. An example is given.