Exciton–exciton-interaction two-dimensional (EEI2D) spectroscopy is a fifth-order variant of 2D electronic spectroscopy. It can be used to probe biexciton dynamics in molecular systems and to observe exciton diffusion in extended systems such as polymers or light-harvesting complexes. The exciton transport strongly depends on the geometrical and energetic landscape and its perturbations. These can be of both local character, such as molecular orientation and energetic disorder, and long-range character, such as polymer kinks and structural domains. In the present theoretical work, we investigate the anisotropy in EEI2D spectroscopy. We introduce a general approach for how to calculate the anisotropy by using the response-function formalism in an efficient way. In numerical simulations, using a Frenkel exciton model with Redfield-theory dynamics, we demonstrate how the measurement of anisotropy in EEI2D spectroscopy can be used to identify various geometrical effects on exciton transport in dimers and polymers. Investigating a molecular heterodimer as an example, we demonstrate the utility of anisotropy in EEI2D spectroscopy for disentangling dynamic localization and annihilation. We further calculate the annihilation in extended systems such as conjugated polymers. In a polymer, a change in the anisotropy provides a unique signature for exciton transport between differently oriented sections. We analyze three types of geometry variations in polymers: a kink, varying geometric and energetic disorder, and different geometric domains. Our findings underline that employing anisotropy in EEI2D spectroscopy provides a way to distinguish between different geometries and can be used to obtain a better understanding of long-range exciton transport.

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