Charge-displacement (CD) analysis has recently proven to be a simple and powerful scheme for quantitatively analyzing the profile the charge redistribution occurring upon intermolecular interactions along a given interaction axis. However, when two molecular fragments bind through complex interactions involving multiple concurrent charge flows, ordinary CD analysis is capable of providing only an averaged picture of the related charge-flow profiles and no detailed information on each of them. In this article, we combine CD analysis with a Hirshfeld partitioning of the molecular charge redistribution for a local analysis on focused portions of the molecule, allowing for a detailed characterization of one charge flow at a time. The resulting scheme-the local charge-displacement (LCD) analysis-is tested on the intriguing case of the dimethyl sulfide-sulfur dioxide complex, characterized by concurrent charge flows relating to a sulfur-sulfur homochalcogen interaction and a pair of hydrogen bonds. The LCD scheme is then applied to the analysis of multiple hydrogen bonding in the acetic acid dimer, of base-pairing interactions in DNA, and of ambifunctional hydrogen bonding in the ammonia-pyridine complex.