How can the complexity of ML-enabled systems be managed effectively? The goal of this research is to investigate how complexity affects ML-Enabled Systems (MLES). To address this question, this research aims to introduce a metrics-based architectural model to characterize the complexity of MLES. The goal is to support architectural decisions, providing a guideline for the inception and growth of these systems. This paper showcases the first step for creating the metrics-based architectural model: an extension of a reference architecture that can describe MLES to collect their metrics.