The challenge of designing interstellar messages capable of being understood by extraterrestrial intelligences (ETI) of unknown cognitive architectures represents one of the most profound problems in exosemiotics. Current approaches to messaging extraterrestrial intelligence (METI) typically assume either a monolithic message structure or simple layered progression. This paper introduces Adaptive Polysemic Messaging (APM), a unified theoretical framework that synthesizes three historically distinct communication paradigms: steganographic concealment, polysemic encoding, and stratified messaging. The APM framework enables the construction of messages that simultaneously: (1) contain multiple semantically coherent interpretations accessible at different cognitive levels, (2) reveal progressively deeper meanings as receiver sophistication increases, and (3) optimize interpretation fidelity for heterogeneous receiver populations from a single transmission. We provide formal mathematical definitions, axiomatize the framework's foundational principles, specify a complete protocol for APM message construction, and discuss implications for both active SETI initiatives and the broader field of xenolinguistics. The framework represents a novel contribution at the intersection of information theory, hermeneutics, and astrobiology.