The advancement of open architecture ecosystems is fundamentally dependent on the interoperability, scalability, and adaptability of their constituent elements. As machine learning (ML) systems become increasingly integral to these ecosystems, the need for a systematic approach to engineer, deploy, and re-engineer them grows. This paper presents a novel modeling approach based on recently published, formal, systems-theoretic models of learning systems. These models serve dual purposes: first, they give a theoretical grounding to standards that govern the architecture, functionality, and performance criteria for ML systems; second, they allow for requirements to be specified at various levels of abstraction to ensure the systems are intrinsically aligned with the overall objectives of the open architecture ecosystem they belong to. Through the proposed modeling approach, we demonstrate how the adoption of standardized models can significantly enhance interoperability between disparate machine learning systems and other architectural components. Further, we relate our framework to on-going efforts such as Open Neural Network Exchange (ONNX). We identify how our approach can be used to address limitations in government acquisition processes for ML systems. The proposed systems-theoretic framework provides a structured methodology that contributes to the foundational building blocks for open architecture ecosystems for ML systems, thereby advancing the state-of-the-art in complex system integration.