Self-supervised learning (SSL) for clinical time series data has received significant attention in recent literature, since these data are highly rich and provide important information about a patient's physiological state. However, most existing SSL methods for clinical time series are limited in that they are designed for unimodal time series, such as a sequence of structured features (e.g., lab values and vitals signs) or an individual high-dimensional physiological signal (e.g., an electrocardiogram). These existing methods cannot be readily extended to model time series that exhibit multimodality, with structured features and high-dimensional data being recorded at each timestep in the sequence. In this work, we address this gap and propose a new SSL method --- Sequential Multi-Dimensional SSL --- where a SSL loss is applied both at the level of the entire sequence and at the level of the individual high-dimensional data points in the sequence in order to better capture information at both scales. Our strategy is agnostic to the specific form of loss function used at each level -- it can be contrastive, as in SimCLR, or non-contrastive, as in VICReg. We evaluate our method on two real-world clinical datasets, where the time series contains sequences of (1) high-frequency electrocardiograms and (2) structured data from lab values and vitals signs. Our experimental results indicate that pre-training with our method and then fine-tuning on downstream tasks improves performance over baselines on both datasets, and in several settings, can lead to improvements across different self-supervised loss functions.