With predictive models becoming prevalent, companies are expanding the types of data they gather. As a result, the collected datasets consist not only of simple numerical features but also more complex objects such as time series, images, or graphs. Such multi-modal data have the potential to improve performance in predictive tasks like outlier detection, where the goal is to identify objects deviating from the main data distribution. However, current outlier detection algorithms are dedicated to individual types of data. Consequently, working with mixed types of data requires either fusing multiple data-specific models or transforming all of the representations into a single format, both of which can hinder predictive performance. In this paper, we propose a multi-modal outlier detection algorithm called Random Similarity Isolation Forest. Our method combines the notions of isolation and similarity-based projection to handle datasets with mixtures of features of arbitrary data types. Experiments performed on 47 benchmark datasets demonstrate that Random Similarity Isolation Forest outperforms five state-of-the-art competitors. Our study shows that the use of multiple modalities can indeed improve the detection of anomalies and highlights the need for new outlier detection benchmarks tailored for multi-modal algorithms.