In an earlier short paper [Phys. Rev. Lett. 120, 101301 (2018)], I argued that the horizonpreserving diffeomorphisms of a generic black hole are enhanced to a larger three-dimensional Bondi-Metzner-Sachs symmetry, which is powerful enough to determine the Bekenstein-Hawking entropy. Here, I provide details and extensions of that argument, including a loosening of horizon boundary conditions and a more thorough treatment of dimensional reduction and meaning of a "near-horizon symmetry."