The diagnosis of the presence of metastatic lymph nodes from abdominal computed tomography (CT) scans is an essential task performed by radiologists to guide radiation and chemotherapy treatment. State-of-the-art deep learning classifiers trained for this task usually rely on a training set containing CT volumes and their respective image-level (i.e., global) annotation. However, the lack of annotations for the localisation of the regions of interest (ROIs) containing lymph nodes can limit classification accuracy due to the small size of the relevant ROIs in this problem. The use of lymph node ROIs together with global annotations in a multi-task training process has the potential to improve classification accuracy, but the high cost involved in obtaining the ROI annotation for the same samples that have global annotations is a roadblock for this alternative. We address this limitation by introducing a new training strategy from two data sets: one containing the global annotations, and another (publicly available) containing only the lymph node ROI localisation. We term our new strategy semi-supervised multi-domain multi-task training, where the goal is to improve the diagnosis accuracy on the globally annotated data set by incorporating the ROI annotations from a different domain. Using a private data set containing global annotations and a public data set containing lymph node ROI localisation, we show that our proposed training mechanism improves the area under the ROC curve for the classification task compared to several training method baselines.