Conceptual models need to be comprehensible and maintainable by humans to exploit their full value in faithfully representing a subject domain. Modularization, i.e. breaking down the monolithic model into smaller, comprehensible chunks has proven very valuable to maintain this value even for very large models. The quality of modularization however often depends on application-specific requirements, the domain, and the modeling language. A well-defined generic modularizing framework applicable to different modeling languages and requirements is lacking. In this paper, we present a customizable and generic multi-objective conceptual models modularization framework. The multi-objective aspect supports addressing heterogeneous requirements while the framework’s genericity supports modularization for arbitrary modeling languages and its customizability is provided by adopting the modularization configuration up to the level of using user-defined heuristics. Our approach applies genetic algorithms to search for a set of optimal solutions. In this paper, we present the details of our Generic Genetic Modularization Framework with a case study to show i) the feasibility of our approach by modularizing models from multiple modeling languages, ii) the customizability by using different objectives for the modularization quality, and, finally, iii) a comparative performance evaluation of our approach on a dataset of ER and ECore models.