Multistability in the intermittent generalized synchronization regime in unidirectionally coupled chaotic systems has been found. To study such a phenomenon, the method for revealing the existence of multistable states in interacting systems being the modification of an auxiliary system approach has been proposed. The efficiency of the method has been testified using the examples of unidirectionally coupled logistic maps and Rössler systems being in the intermittent generalized synchronization regime. The quantitative characteristic of multistability has been introduced into consideration.