An internal model is a neural mechanism that can mimic the input-output properties of a controlled object such as a tool. Recent research interests have moved on to how multiple internal models are learned and switched under a given context of behavior. Two representative computational models for task switching propose distinct neural mechanisms, thus predicting different brain activity patterns in the switching of internal models. In one model, called the mixture-of-experts architecture, switching is commanded by a single executive called a "gating network," which is different from the internal models. In the other model, called the MOSAIC (MOdular Selection And Identification for Control), the internal models themselves play crucial roles in switching. Consequently, the mixture-of-experts model predicts that neural activities related to switching and internal models can be temporally and spatially segregated, whereas the MOSAIC model predicts that they are closely intermingled. Here, we directly examined the two predictions by analyzing functional magnetic resonance imaging activities during the switching of one common tool (an ordinary computer mouse) and two novel tools: a rotated mouse, the cursor of which appears in a rotated position, and a velocity mouse, the cursor velocity of which is proportional to the mouse position. The switching and internal model activities temporally and spatially overlapped each other in the cerebellum and in the parietal cortex, whereas the overlap was very small in the frontal cortex. These results suggest that switching mechanisms in the frontal cortex can be explained by the mixture-of-experts architecture, whereas those in the cerebellum and the parietal cortex are explained by the MOSAIC model.