Remote epitaxy has drawn attention as it offers epitaxy of functional materials that can be released from the substrates with atomic precision, thus enabling production and heterointegration of flexible, transferrable, and stackable freestanding single-crystalline membranes. In addition, the remote interaction of atoms and adatoms through two-dimensional (2D) materials in remote epitaxy allows investigation and utilization of electrical/chemical/physical coupling of bulk (3D) materials via 2D materials (3D–2D–3D coupling). Here, we unveil the respective roles and impacts of the substrate material, graphene, substrate–graphene interface, and epitaxial material for electrostatic coupling of these materials, which governs cohesive ordering and can lead to single-crystal epitaxy in the overlying film. We show that simply coating a graphene layer on wafers does not guarantee successful implementation of remote epitaxy, since atomically precise control of the graphene-coated interface is required, and provides key considerations for maximizing the remote electrostatic interaction between the substrate and adatoms. This was enabled by exploring various material systems and processing conditions, and we demonstrate that the rules of remote epitaxy vary significantly depending on the ionicity of material systems as well as the graphene–substrate interface and the epitaxy environment. The general rule of thumb discovered here enables expanding 3D material libraries that can be stacked in freestanding form.