The techniques developed in this paper for commutative N-polyregular functions can potentially be extended to other subclasses of rational series, such as weighted automata or formal power series. By adapting the concepts and methodologies used in the study of commutative N-polyregular functions, it may be possible to analyze and characterize the behavior of functions in these related subclasses. The key insights and results obtained in this work, such as the construction of canonical models of computation and the characterization of function classes, can serve as a foundation for exploring and understanding the properties of other rational series subclasses. This extension could lead to a deeper understanding of the relationships between different classes of functions and their decision problems.