Data-driven discovery of image-derived phenotypes (IDPs) from large-scale multimodal brain imaging data has enormous potential for neuroscientific and clinical research by linking IDPs to subjects' demographic, behavioural, clinical and cognitive measures (i.e., non-imaging derived phenotypes or nIDPs). However, current approaches are primarily based on unsupervised approaches, without the use of information in nIDPs. In this paper, we proposed a semi-supervised, multimodal, and multi-task fusion approach, termed SuperBigFLICA, for IDP discovery, which simultaneously integrates information from multiple imaging modalities as well as multiple nIDPs. SuperBigFLICA is computationally efficient and largely avoids the need for parameter tuning. Using the UK Biobank brain imaging dataset with around 40,000 subjects and 47 modalities, along with more than 17,000 nIDPs, we showed that SuperBigFLICA enhances the prediction power of nIDPs, benchmarked against IDPs derived by conventional expert-knowledge and unsupervised-learning approaches (with average nIDP prediction accuracy improvements of up to 46%). It also enables the learning of generic imaging features that can predict new nIDPs. Further empirical analysis of the SuperBigFLICA algorithm demonstrates its robustness in different prediction tasks and the ability to derive biologically meaningful IDPs in predicting health outcomes and cognitive nIDPs, such as fluid intelligence and hypertension.