To ensure that secure applications do not leak their secrets, they are required to uphold several security properties such as spatial and temporal memory safety as well as cryptographic constant time. Existing work shows how to enforce these properties individually, in an architecture-independent way, by using secure compiler passes that each focus on an individual property. Unfortunately, given two secure compiler passes that each preserve a possibly different security property, it is unclear what kind of security property is preserved by the composition of those secure compiler passes. This paper is the first to study what security properties are preserved across the composition of different secure compiler passes. Starting from a general theory of property composition for security-relevant properties (such as the aforementioned ones), this paper formalises a theory of composition of secure compilers. Then, it showcases this theory a secure multi-pass compiler that preserves the aforementioned security-relevant properties. Crucially, this paper derives the security of the multi-pass compiler from the composition of the security properties preserved by its individual passes, which include security-preserving as well as optimisation passes. From an engineering perspective, this is the desirable approach to building secure compilers.