Multi-reader multi-case (MRMC) studies are often used for the evaluation of medical imaging devices. Due to limited prior information, the sizing of such studies (i.e., sizing both readers and cases) is often inaccurate. It is therefore desirable to adaptively resize the study towards a target power after an interim analysis of the study data. The major statistical concern for sample size re-estimation based on the interim analysis is the inflation of type I error rate. We developed methods that, based upon the observed data at the interim analysis, simultaneously resize the study towards a target power and adaptively adjust the critical value for the final hypothesis testing to control the type I error rate. Our methodologies apply to commonly used study endpoints including the area under the ROC curve (AUC), sensitivity, and specificity. Simulation studies show our methods can boost the statistical power to a target value by resizing the study after an interim analysis while controlling the type I error rate at the nominal level. We have developed a freely available R software package for the design and analysis of adaptive MRMC studies.