Backdoor attacks have emerged as a primary threat to (pre-)training and deployment of deep neural networks (DNNs). While backdoor attacks have been extensively studied in a body of works, most of them were focused on single-trigger attacks that poison a dataset using a single type of trigger. Arguably, real-world backdoor attacks can be much more complex, e.g., the existence of multiple adversaries for the same dataset if it is of high value. In this work, we investigate the practical threat of backdoor attacks under the setting of \textbf{multi-trigger attacks} where multiple adversaries leverage different types of triggers to poison the same dataset. By proposing and investigating three types of multi-trigger attacks, including parallel, sequential, and hybrid attacks, we provide a set of important understandings of the coexisting, overwriting, and cross-activating effects between different triggers on the same dataset. Moreover, we show that single-trigger attacks tend to cause overly optimistic views of the security of current defense techniques, as all examined defense methods struggle to defend against multi-trigger attacks. Finally, we create a multi-trigger backdoor poisoning dataset to help future evaluation of backdoor attacks and defenses. Although our work is purely empirical, we hope it can help steer backdoor research toward more realistic settings.