The success of deep learning relies heavily on large datasets with extensive labels, but we often only have access to several small, heterogeneous datasets associated with partial labels, particularly in the field of medical imaging. When learning from multiple datasets, existing challenges include incomparable, heterogeneous, or even conflicting labeling protocols across datasets. In this paper, we propose a new initiative--"data, assemble"--which aims to unleash the full potential of partially labeled data and enormous unlabeled data from an assembly of datasets. To accommodate the supervised learning paradigm to partial labels, we introduce a dynamic adapter that encodes multiple visual tasks and aggregates image features in a question-and-answer manner. Furthermore, we employ pseudo-labeling and consistency constraints to harness images with missing labels and to mitigate the domain gap across datasets. From proof-of-concept studies on three natural imaging datasets and rigorous evaluations on two large-scale thorax X-ray benchmarks, we discover that learning from "negative examples" facilitates both classification and segmentation of classes of interest. This sheds new light on the computer-aided diagnosis of rare diseases and emerging pandemics, wherein "positive examples" are hard to collect, yet "negative examples" are relatively easier to assemble. As a result, besides exceeding the prior art in the NIH ChestXray benchmark, our model is particularly strong in identifying diseases of minority classes, yielding over 3-point improvement on average. Remarkably, when using existing partial labels, our model performance is on-par (p>0.05) with that using a fully curated dataset with exhaustive labels, eliminating the need for additional 40% annotation costs.