"How do witnesses make identification decisions when viewing a lineup?" Understanding the witness decision-making process is essential for researchers to develop methods that can reduce mistaken identifications and improve lineup practices. Yet, the inclusion of fillers has posed a pivotal challenge to this task because the traditional signal detection theory is only applicable to binary decisions and cannot easily incorporate lineup fillers. This paper proposes a multi-item signal detection theory (mSDT) model to help understand the witness decision-making process. The mSDT model clarifies the importance of considering the joint distributions of suspect and filler signals. The model also visualizes the joint distributions in a multivariate decision space, which allows for the incorporation of all eyewitness responses, including suspect identifications, filler identifications, and rejections. The paper begins with a set of simple assumptions to develop the mSDT model and then explores alternative assumptions that can potentially accommodate more sophisticated considerations. The paper further discusses the implications of the mSDT model. With a mathematical modeling and visualization approach, the mSDT model provides a novel theoretical framework for understanding eyewitness identification decisions and addressing debates around eyewitness SDT and ROC applications.