Online Continual Learning (OCL) methods train a model on a non-stationary data stream where only a few examples are available at a time, often leveraging replay strategies. However, usage of replay is sometimes forbidden, especially in applications with strict privacy regulations. Therefore, we propose Continual MultiPatches (CMP), an effective plug-in for existing OCL self-supervised learning strategies that avoids the use of replay samples. CMP generates multiple patches from a single example and projects them into a shared feature space, where patches coming from the same example are pushed together without collapsing into a single point. CMP surpasses replay and other SSL-based strategies on OCL streams, challenging the role of replay as a go-to solution for self-supervised OCL.