There have been many extreme fire seasons in Maritime Southeast Asia (MSEA) over the last two decades, a trend which will likely continue or accelerate due to climate change. Fires, in turn, are a major driver of atmospheric carbon monoxide (CO) variability, especially in the Southern Hemisphere. Here we attempt to maximize the amount of CO variability that can be explained via human-interpretable statistical models that use only climate mode indices as predictor variables. We expand upon previous work through the complexity at which we study the connections between climate mode indices and atmospheric CO (a proxy for fire intensity). Specifically, we present three modeling advancements. First, we analyze five different climate modes at a weekly timescale, which increases explained variability by 15% over models on a monthly timescale. Second, we accommodate multiple lead times for each climate mode index, finding that some indices have very different effects on CO at different lead times. Finally, we model the interactions between climate mode indices at weekly timescales, which provides a framework for studying these interactions at a higher level of complexity than previous work. Furthermore, we perform a stability analysis and show that our model for the MSEA region is robust, which adds weight to the scientific interpretation of the selected model terms. We believe that the complex relationships quantified here will be useful for scientists studying modes of variability in MSEA and for forecasters looking to maximize the information they glean from climate modes.