The realization of air-stable 2D metals epitaxial to SiC and capped by graphene creates a potentially immense chemical space of 2D metals and alloys that could expand the variety of solid-state excitations unique to 2D metals beyond what is known for graphene and niobium/tantalum chalcogenides. We perform a high-throughput computational survey from first-principles predicting the structures and stabilities of all metals in the periodic table when they intercalate graphene/SiC. Our results not only agrees with all experimentally known metal/SiC structures explored so far, but also reveals conspicuous trends related to metal cohesive energies and metal-silicon bonding. For special groups of metals, a small bandgap opens, relying on appropriate electron filling and substrate-induced symmetry breaking. From this gapping stabilization, we derive alloying rules unique to 2D metals.