Multitask learning (MTL) using electronic health records allows concurrent prediction of multiple endpoints. MTL has shown promise in improving model performance and training efficiency; however, it often suffers from negative transfer - impaired learning if tasks are not appropriately selected. We introduce a sequential subnetwork routing (SeqSNR) architecture that uses soft parameter sharing to find related tasks and encourage cross-learning between them. Using the MIMIC-III (Medical Information Mart for Intensive Care-III) dataset, we train deep neural network models to predict the onset of 6 endpoints including specific organ dysfunctions and general clinical outcomes: acute kidney injury, continuous renal replacement therapy, mechanical ventilation, vasoactive medications, mortality, and length of stay. We compare single-task (ST) models with naive multitask and SeqSNR in terms of discriminative performance and label efficiency. SeqSNR showed a modest yet statistically significant performance boost across 4 of 6 tasks compared with ST and naive multitasking. When the size of the training dataset was reduced for a given task (label efficiency), SeqSNR outperformed ST for all cases showing an average area under the precision-recall curve boost of 2.1%, 2.9%, and 2.1% for tasks using 1%, 5%, and 10% of labels, respectively. The SeqSNR architecture shows superior label efficiency compared with ST and naive multitasking, suggesting utility in scenarios in which endpoint labels are difficult to ascertain. © The Author(s) 2021. Published by Oxford University Press on behalf of the American Medical Informatics Association.