Machine learning (ML) models are proving to be vulnerable to a variety of attacks that allow the adversary to learn sensitive information, cause mispredictions, and more. While these attacks have been extensively studied, current research predominantly focuses on analyzing each attack type individually. In practice, however, adversaries may employ multiple attack strategies simultaneously rather than relying on a single approach. This prompts a crucial yet underexplored question: When the adversary has multiple attacks at their disposal, are they able to mount or amplify the effect of one attack with another? In this paper, we take the first step in studying the strategic interactions among different attacks, which we define as attack compositions. Specifically, we focus on four well-studied attacks during the model's inference phase: adversarial examples, attribute inference, membership inference, and property inference. To facilitate the study of their interactions, we propose a taxonomy based on three stages of the attack pipeline: preparation, execution, and evaluation. Using this taxonomy, we identify four effective attack compositions, such as property inference assisting attribute inference at its preparation level and adversarial examples assisting property inference at its execution level. We conduct extensive experiments on the attack compositions using three ML model architectures and three benchmark image datasets. Empirical results demonstrate the effectiveness of these four attack compositions. We implement and release a modular reusable toolkit, COAT. Arguably, our work serves as a call for researchers and practitioners to consider advanced adversarial settings involving multiple attack strategies, aiming to strengthen the security and robustness of AI systems.