Medical studies are usually time consuming, cumbersome and extremely costly to perform, and for exploratory research, their results are also difficult to predict a priori. This is particularly the case for rare diseases, for which finding enough patients is difficult and usually requires an international-scale research. In this case, the process can be even more difficult due to the heterogeneity of data-protection regulations, making the data sharing process particularly hard. In this short paper, we propose MedCo2 (pronounced MedCo square), a distributed system that streamlines the process of a medical study by bridging and enabling both data discovery and data analysis among multiple databases, while protecting data confidentiality and patients' privacy. MedCo2 relies on interactive protocols, homomorphic encryption and differential privacy. It enables the privacy-preserving computations of multiple statistics such as cosine similarity and variance, and the training of machine learning models, on patients that are obliviously selected according to specific criteria among multiple databases.