Occupancy models are commonly used in statistical ecology to model binary detection/non-detection data. These hierarchical models make a distinction between detection/non-detection and presence/absence by treating true occupancy as a latent process. In this paper, we propose a multi-species, multi-season occupancy model to jointly model detection/non-detection data on multiple species. Existing literature has shown that models which account for various sources of dependence in the latent occupancy process improve estimation, especially in the single-survey setting. However, the detection process in the model has not received much attention, even though detectability of a species is expected to relate to the detectability of other species and to detectability in previous time periods. In this work, we propose a model to capture this phenomenon by incorporating a multivariate temporal random effect in the detection process. We perform a simulation study to show that the proposed model yields more accurate estimates of regression effects and probabilities as compared to models that only use covariates to quantify detection. We apply our model to detection/non-detection data on three species – Thomson’s gazelle, zebra, and wildebeest – in Serengeti National Park of Tanzania, Africa.