Multilingual automatic speech recognition (ASR) models have shown great promise in recent years because of the simplified model training and deployment process. Conventional methods either train a universal multilingual model without taking any language information or with a 1-hot language ID (LID) vector to guide the recognition of the target language. In practice, the user can be prompted to pre-select several languages he/she can speak. The multilingual model without LID cannot well utilize the language information set by the user while the multilingual model with LID can only handle one pre-selected language. In this paper, we propose a novel configurable multilingual model (CMM) which is trained only once but can be configured as different models based on users' choices by extracting language-specific modules together with a universal model from the trained CMM. Particularly, a single CMM can be deployed to any user scenario where the users can pre-select any combination of languages. Trained with 75K hours of transcribed anonymized Microsoft multilingual data and evaluated with 10-language test sets, the proposed CMM improves from the universal multilingual model by 26.0%, 16.9%, and 10.4% relative word error reduction when the user selects 1, 2, or 3 languages, respectively. CMM also performs significantly better on code-switching test sets.