Multi-task learning (MTL) is a machine learning technique aiming to improve model performance by leveraging information across many tasks. It has been used extensively on various data modalities, including electronic health record (EHR) data. However, despite significant use on EHR data, there has been little systematic investigation of the utility of MTL across the diverse set of possible tasks and training schemes of interest in healthcare. In this work, we examine MTL across a battery of tasks on EHR time-series data. We find that while MTL does suffer from common negative transfer, we can realize significant gains via MTL pre-training combined with single-task fine-tuning. We demonstrate that these gains can be achieved in a task-independent manner and offer not only minor improvements under traditional learning, but also notable gains in a few-shot learning context, thereby suggesting this could be a scalable vehicle to offer improved performance in important healthcare contexts.