The Cosmic Web contains filamentary structure on a wide range of scales. On the largest scales, superclustering aligns multiple galaxy clusters along inter-cluster bridges, visible through their thermal Sunyaev-Zel'dovich signal in the Cosmic Microwave Background. We demonstrate a new, flexible method to analyze the hot gas signal from multi-scale extended structures. We use a Compton-y map from the Atacama Cosmology Telescope (ACT) stacked on redMaPPer cluster positions from the optical Dark Energy Survey (DES). Cutout images from the y map are oriented with large-scale structure information from DES galaxy data such that the superclustering signal is aligned before being overlaid. We find evidence for an extended quadrupole moment of the stacked y signal at the 3.5σ level, demonstrating that the large-scale thermal energy surrounding galaxy clusters is anisotropically distributed. We compare our ACT×DES results with the Buzzard simulations, finding broad agreement. Using simulations, we highlight the promise of this novel technique for constraining the evolution of anisotropic, non-Gaussian structure using future combinations of microwave and optical surveys.