Using multiple, individual encryption schemes is a well-established method to increase the overall security of encrypted data. These so-called multiple encryption or hybrid schemes have regained traction in the context of public-key cryptography due to the rise of quantum computers, since it allows the combination of well-known classical encryption schemes with novel post-quantum schemes. In this paper, we conduct a survey of the state-of-the-art public-key multiple encryption (M-PKE) schemes. For the first time, we describe the most relevant M-PKE schemes in detail and discuss their security in a unified model, which allows better comparison between the schemes. Hence, we compare the security, efficiency, and complexity of the schemes and offer recommendations for usage based on common use cases. Our survey emphasizes the importance of being deliberate when combining encryption schemes, as small nuances can easily break security.