We propose an extremely simple and highly effective approach to faithfully combine different object detectors to obtain a Mixture of Experts (MoE) that has a superior accuracy to the individual experts in the mixture. We find that naively combining these experts in a similar way to the well-known Deep Ensembles (DEs), does not result in an effective MoE. We identify the incompatibility between the confidence score distribution of different detectors to be the primary reason for such failure cases. Therefore, to construct the MoE, our proposal is to first calibrate each individual detector against a target calibration function. Then, filter and refine all the predictions from different detectors in the mixture. We term this approach as MoCaE and demonstrate its effectiveness through extensive experiments on object detection, instance segmentation and rotated object detection tasks. Specifically, MoCaE improves (i) three strong object detectors on COCO test-dev by $2.4$ $\mathrm{AP}$ by reaching $59.0$ $\mathrm{AP}$; (ii) instance segmentation methods on the challenging long-tailed LVIS dataset by $2.3$ $\mathrm{AP}$; and (iii) all existing rotated object detectors by reaching $82.62$ $\mathrm{AP_{50}}$ on DOTA dataset, establishing a new state-of-the-art (SOTA). Code will be made public.