Complex oxide heterostructures display some of the most chemically abrupt, atomically precise interfaces, which is advantageous when constructing new interface phases with emergent properties by juxtaposing incompatible ground states. One might assum
e that atomically precise interfaces result from stoichiometric growth, but here we show that the most precise control is obtained for non-stoichiometric growth where differing surface energies can be compensated by surfactant-like effects. For the precise growth of Sr$_{n+1}$Ti$_n$O$_{3n+1}$ Ruddlesden-Popper (RP) phases, stoichiometric deposition leads to the loss of the first RP rock-salt double layer, but growing with a strontium-rich surface layer restores the bulk stoichiometry and ordering of the subsurface RP structure. Our results dramatically expand the materials that can be prepared in epitaxial heterostructures with precise interface control---from just the $n=infty$ end members (perovskites) to the entire RP family---enabling the exploration of novel quantum phenomena at a richer variety of oxide interfaces.
