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A multimorbidity trajectory charts the time-dependent acquisition of disease conditions in an individual. This is important for understanding and managing patients who have a complex array of multiple chronic conditions, particularly later in life. We have developed a model based on a Bayesian nonparametric feature allocation model with a Wright--Fisher Indian Buffet Process prior. Our model, which we call the Multimorbidity Wright--Fisher Indian Buffet Process (m-WFIBP) defines a generative process in which a set of diseases of an individual is drawn from latent multimorbidity clusters whose dependency structure across time is governed by the Wright--Fisher diffusion. We demonstrate the utility of our model in applications to simulated data and disease event data from patient electronic health records. In both settings, we show how the m-WFIBP can obtain intelligible representation of latent multimorbidity clusters and its time susceptibility and predict future disease acquisition.