As machine learning (ML) techniques are being increasingly used in many applications, their vulnerability to adversarial attacks becomes well-known. Test time attacks, usually launched by adding adversarial noise to test instances, have been shown effective against the deployed ML models. In practice, one test input may be leveraged by different ML models. Test time attacks targeting a single ML model often neglect their impact on other ML models. In this work, we empirically demonstrate that naively attacking the classifier learning one concept may negatively impact classifiers trained to learn other concepts. For example, for the online image classification scenario, when the Gender classifier is under attack, the (wearing) Glasses classifier is simultaneously attacked with the accuracy dropped from 98.69 to 88.42. This raises an interesting question: is it possible to attack one set of classifiers without impacting the other set that uses the same test instance? Answers to the above research question have interesting implications for protecting privacy against ML model misuse. Attacking ML models that pose unnecessary risks of privacy invasion can be an important tool for protecting individuals from harmful privacy exploitation. In this paper, we address the above research question by developing novel attack techniques that can simultaneously attack one set of ML models while preserving the accuracy of the other. In the case of linear classifiers, we provide a theoretical framework for finding an optimal solution to generate such adversarial examples. Using this theoretical framework, we develop a multi-concept attack strategy in the context of deep learning. Our results demonstrate that our techniques can successfully attack the target classes while protecting the protected classes in many different settings, which is not possible with the existing test-time attack-single strategies.