To date, most studies of neural representation have focused on how a single stimulus is encoded in the spiking activity of neurons. Consequently, little is known about how sensory neurons can preserve information from multiple stimuli – a problem given that many sensory neurons have relatively broad receptive fields. Multiplexing is a neural encoding theory that posits that neurons temporally switch between encoding various stimuli when more than one stimulus is present. To date, the strongest statistical evidence for this theory comes from spike counts measured over long time windows, leading to circumstantial evidence and no insight into the time scale of the switching process. Here, we construct a statistically falsifiable single-neuron model for multiplexing at the spike train level to address this gap. The multiplexing model posits that the switching behavior arises as a result of a competition process between the stimuli, which are modeled using drift-diffusion processes. Crucially, this model allows us to utilize spike-timing information, which offers novel insight into the timescale at which switching occurs. In addition to a multiplexing-specific model, we develop alternative models that represent alternative encoding theories with some level of abstraction. Using information criteria, we perform model comparison to determine whether the data favor multiplexing over alternative theories of neural encoding. Using data recorded from the inferior colliculus of two macaque monkeys, we report compelling evidence of multiplexing and suggest that the switching process may occur faster than previously suspected.