The mechanism of switching activity patterns in a central pattern generator is fundamental to the generation of diverse motor behaviors. Based on what is known about a brainstem substrate mediating the oral components of ingestion and rejection, we use computational techniques to construct a hypothetical multifunctional network that switches between the motor outputs of ingestion (licking) and rejection (gaping). The network was constructed using single-compartment conductance-based models for individual neurons based on Hodgkin-Huxley formalism. Using a fast-slow reduction and geometric analysis we describe a mechanism for pattern switching between licks and gapes. The model supports the hypothesis that a single configuration of network connections can produce both activity patterns. It further predicts that prolonged inhibition of some network neurons could lead to a switch in network activity from licks to gapes.