Recently, there has been much interest in gene-disease networks and polypharmacology as a basis for drug repositioning. Here, we integrate data from structural and chemical databases to create a drug-target-disease network for 147 promiscuous drugs, their 553 protein targets, and 44 disease indications. Visualizing and analyzing such complex networks is still an open problem. We approach it by mining the network for network motifs of bi-cliques. In our case, a bi-clique is a subnetwork in which every drug is linked to every target and disease. Since the data are incomplete, we identify incomplete bi-cliques, whose completion introduces novel, predicted links from drugs to targets and diseases. We demonstrate the power of this approach by repositioning cardiovascular drugs to parasitic diseases, by predicting the cancer-related kinase PIK3CG as a novel target of resveratrol, and by identifying for five drugs a shared binding site in four serine proteases and novel links to cancer, cardiovascular, and parasitic diseases.