Performance is often impaired when at least two tasks are executed simultaneously. This constitutes an issue because many everyday tasks, e.g., cooking and driving, require conducting several subtasks in parallel. This raises the question of whether it is possible to explain and prevent this effect. The underlying mechanism thereof is hotly debated: e.g., (cognitive) capacity limitations, an increased demand for cognitive control, or impaired cognitive processing are discussed as constraints of multitasking. Hereby, multitasking performance has been traditionally operationalized based on difference scores between single- and multi-task condition performance measures or performance in multitasking conditions only. However, these approaches do not provide an algorithmic solution to multitasking and therefore provide little information as to how multitasking decrements emerge. Computational modeling constitutes a powerful solution to this issue. We used and extended a computational modeling framework based on the theory of visual attention by Bayesian asymmetrical distribution and mixture modeling to explain how performance declines in dual- and triple-task conditions as a function of sensory cognitive load. For this, we assessed and analyzed math, auditory discrimination, and working memory performance measures in single- and multi-task conditions of 60 individuals. By comparing the outcomes of a traditional and our approach of analyzing these performance measures, we demonstrate that in addition to replicating established multitasking performance effects our approach also allows to pinpoint how multitasking decrements emerge: e.g., we show that modality-specific cognitive overload impairs information processing only in some individuals, which may explain inconsistent results regarding cognitive capacity limitations in the literature.