Contrastive, self-supervised learning (SSL) is used to train a model that predicts cancer type from miRNA, mRNA or RPPA expression data. This model, a pretrained FT-Transformer, is shown to outperform XGBoost and CatBoost, standard benchmarks for tabular data, when labelled samples are scarce but the number of unlabelled samples is high. This is despite the fact that the datasets we use have $\mathcal{O}(10^{1})$ classes and $\mathcal{O}(10^{2})-\mathcal{O}(10^{4})$ features. After demonstrating the efficacy of our chosen method of self-supervised pretraining, we investigate SSL for multi-modal models. A late-fusion model is proposed, where each omics is passed through its own sub-network, the outputs of which are averaged and passed to the pretraining or downstream objective function. Multi-modal pretraining is shown to improve predictions from a single omics, and we argue that this is useful for datasets with many unlabelled multi-modal samples, but few labelled unimodal samples. Additionally, we show that pretraining each omics-specific module individually is highly effective. This enables the application of the proposed model in a variety of contexts where a large amount of unlabelled data is available from each omics, but only a few labelled samples.