We present an extension of the Individual Brain Charting dataset -a high spatial-resolution, multi-task, functional Magnetic Resonance Imaging dataset, intended to support the investigation on the functional principles governing cognition in the human brain. The concomitant data acquisition from the same 12 participants, in the same environment, allows to obtain in the long run finer cognitive topographies, free from inter-subject and inter-site variability. This second release provides more data from psychological domains present in the first release, and also yields data featuring new ones. It includes tasks on e.g. mental time travel, reward, theory-of-mind, pain, numerosity, self-reference effect and speech recognition. In total, 13 tasks with 86 contrasts were added to the dataset and 63 new components were included in the cognitive description of the ensuing contrasts. As the dataset becomes larger, the collection of the corresponding topographies becomes more comprehensive, leading to better brain-atlasing frameworks. This dataset is an open-access facility; raw data and derivatives are publicly available in neuroimaging repositories.