Mutual Information Rate (MIR) is a key tool for quantifying the dynamic coupling between two processes within a network, particularly in the analysis of cardiorespiratory interactions. However, MIR between two processes can vary significantly when considering other processes in the network due to high-order dependencies among system processes. In this study, we exploit a novel approach: conditioning on the processes that maximize or minimize the dynamic coupling. This approach decomposes the maximal MIR into unique, redundant, and synergistic components, allowing the assessment of high-order effects relative to dyadic effects. This approach is initially tested on simulated Gaussian processes that dynamically interact and then applied to cardiovascular and respiratory time series data from healthy subjects at rest and under postural stress. Our findings indicate that cardiorespiratory interactions are predominantly governed by redundancy, underscoring the importance of considering polyadic interactions.