Human multitasking often involves complex task interactions and subtle tradeoffs which might be best understood through detailed computational cognitive modeling, yet traditional cognitive modeling approaches may not explore a sufficient range of task strategies to reveal the true complexity of multitasking behavior. This study proposes a systematic approach for exploring a large number of strategies using a computer-cluster-based parallelized modeling system. The paper demonstrates the efficacy of the approach for investigating and revealing the effects of different microstrategies on human performance, both within and across individuals, for a time-pressured multimodal dual task. The modeling results suggest that multitasking performance is not simply a matter of interleaving cognitive and sensorimotor processing but is instead heavily influenced by the selection of subtask microstrategies.