Can observers access two spatially separated color targets (e.g., red and green) at the same time (i.e., in parallel)? According to the Boolean map theory of visual attention (Huang & Pashler, Psychological Review, 114(3), 599-631, 2007), access to two different features that belong to the same dimension (e.g., red and green targets) is limited and therefore can be held only in a serial fashion. The current study proposes a strong test of the Boolean map theory of attention through the application of two of the most rigorous stochastic approaches to response times modeling-the system factorial technology (Townsend & Nozawa, 1995) and the logical rule models (Fifić, Little, & Nosofsky, Psychological Review, 117, 309-348, 2010). These approaches allowed identification of serial, parallel, and coactive architectures in the processing of multicolor targets. The results showed that multiple-color targets are processed serially when observers are required to process all the targets in the display (i.e., an exhaustive stopping rule), and in parallel or coactively when observers can terminate the search when one of the targets is found (i.e., self-terminating stopping rule). These results are generally inconsistent with predictions of the Boolean map theory. They highlight the role of stopping rules in multicolor visual search, as well as the flexibility of the attentional system in shifting between processing architectures.