In model-driven software engineering, models are used in all phases of the development process. These models may get broken due to various editions during the modeling process. There are a number of existing tools that reduce the burden of manually dealing with correctness issues in models, however, most of these tools do not prioritize customization to follow user requirements nor allow the extension of their components to adapt to different model types. In this paper, we present an extensible model repair framework which enable users to deal with different types of models and to add their own repair preferences to customize the results. The framework uses customizable learning algorithms to automatically find the best sequence of actions for repairing a broken model according to the user preferences. As an example, we customize the framework by including as a preference a model distance metric, which allows the user to choose a more or less conservative repair. Then, we evaluate how this preference extension affects the results of the repair by comparing different distance metric calculations. Our experiment proves that extending the framework makes it more precise and produces models with better quality characteristics.