Heterogeneous interfaces are critical in a wide range of applications, and their material properties can be tuned via changes in the coverage and configuration of chemical adsorbates. However, the tunability of such adlayers is limited by a lack of knowledge surrounding the impact of adsorbate internal structure and rotational symmetry on lateral interactions between coadsorbates. Using density functional theory (DFT) and cluster expansions, we systematically determine the impacts of rotational symmetry on lateral interactions between coadsorbates as a function of DFT functional, adsorbate type, metal type, and cluster configuration. Results indicate that the rotational symmetry effects can be nearly exclusively partitioned into the shortest 2body clusters. By electronic analysis, the nature and strength of such effects on the lateral interactions are attributed to a balance of repulsive and attractive electrostatic interactions that are dependent on the adsorbate and metal types. Taken together, our characterization of the impacts of adsorbate internal structure and rotational symmetry on lateral interactions enables improved accuracy within multiscale modeling of multibody adsorbates at heterogeneous interfaces.