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A thorough understanding of the nature and pattern of intermolecular interactions in molecular aggregates and crystals is a prerequisite for the design of the next generation of functional materials. In systems with multiple, symmetrically equivalent molecules per unit cell, each excited state of the isolated molecule splits into several Davydov components that appear in the absorption spectra in up to three orthogonally polarized transitions. In this work, a Frenkel–Holstein Hamiltonian is adopted to simulate the vibronic structure of the Davydov components in aggregates and crystals with up to four molecules per unit cell, where electrostatic intermolecular interactions define either 1D or 2D structures. Analysis shows that vibronic signatures report directly on the electronic couplings that contribute to the Davydov splitting and the exciton band shapes. Specifically, the vibronic signature of a given Davydov component is solely determined by its free excitonic shift. For crystals with two molecules per unit cell, the lower and upper Davydov components can each exhibit J-like or H-like behavior, resulting in JJ, JH, and HH components in order of increasing energy, all with unique vibronic signatures. Under certain conditions, null points can exist in either band, leading to a monomer-like absorption spectrum for the corresponding Davydov component. In crystals with four symmetrically equivalent molecules per unit cell, the J- or H-nature of the three orthogonally polarized Davydov components results in four possible combinations, JJJ, JJH, JHH, and HHH in order of increasing energy, all readily identified through vibronic signatures.