Connectomics is a popular approach for understanding the brain with neuroimaging data. However, a connectome generated from one atlas is different in size, topology, and scale compared to a connectome generated from another. Consequently, connectomes generated from different atlases cannot be used in the same analysis. This limitation hinders efforts toward increasing sample size and demonstrating generalizability across datasets. Recently, we proposed Cross Atlas Remapping via Optimal Transport (CAROT) to find a spatial mapping between a pair of atlases based on a set of training data. The mapping transforms timeseries fMRI data parcellated with an atlas to form a connectome based on a different one. Crucially, CAROT does not need raw fMRI data and thus does not require re-processing, which can otherwise be time-consuming and expensive. The current CAROT implementation leverages information from several source atlases to create robust mappings for a target atlas. In this work, we extend CAROT to combine existing mappings between a source and target atlas for an arbitrary number of mappings. This extension (labeled Stacking CAROT) allows mappings between a pair of atlases to be created once and re-used with other pre-trained mappings to create new mappings as needed. Reconstructed connectomes from Stacking CAROT perform as well as those from CAROT in downstream analyses. Importantly, Stacking CAROT significantly reduces training time and storage requirements compared to CAROT. Overall, Stacking CAROT improves previous versions of CAROT.