This paper proposes a deep learning model for predicting the next activities in a temporal sequence of activity-events associated with a single process instance. The proposed model is based on a mixture of experts mechanism supported by the Switch-Transformer neural network architecture. The deep learning model is trained from scratch on process enactment event log histories. The ultimate goal is to predict the next activities, generate their probabilities of occurrence, and visualize all the predicted next activities in a graphical form of temporal order representing each running case of the corresponding process model. To assess the operational effectiveness of the proposed model, performance evaluations were conducted on synthetic and real-life process event log datasets typically used in previous research.