With recent advances in multi-color super-resolution light microscopy, it is possible to simultaneously visualize multiple subunits within biological structures at nanometer resolution. To optimally evaluate and interpret spatial proximity of stainings on such an image, colocalization analysis tools have to be able to integrate prior knowledge on the local geometry of the recorded biological complex. We present MultiMatch to analyze the abundance and location of chain-like particle arrangements in multi-color microscopy based on multi-marginal optimal unbalanced transport methodology. Our object-based colocalization model statistically addresses the effect of incomplete labeling efficiencies enabling inference on existent, but not fully observable particle chains. We showcase that MultiMatch is able to consistently recover existing chain structures in three-color STED images of DNA origami nanorulers and outperforms geometry-uninformed triplet colocalization methods in this task. MultiMatch generalizes to an arbitrary number of color channels and is provided as a user-friendly Python package comprising colocalization visualizations.