Plasmons are electronic density fluctuations inside a metal that usually resonate at ultraviolet frequencies. In our studies, we explore how surface and bulk plasmons emerge (or survive) under extreme dimensional confinement. Atomically-smooth ultrathin Mg films were epitaxially grown on Si(111), allowing for atomically-precise tuning of the bulk plasmon response and its bulk-sensitive probing via core-level photoemission. While the single-particle states in these 6-25 monolayer (ML) thick films consist of a series of two-dimensional subbands, the collective response is like that of a thin slice carved from bulk Mg subject to quantum-mechanical boundary conditions. Remarkably, this bulk-like behavior persists all the way down to five monatomic layers. In this low-dimensional crossover regime, plasmon modes are primarily excited via the sudden creation of the core hole as the extrinsic loss channel (which is the dominant channel in the bulk) is strongly suppressed. The collective response of the thinnest films is characterized by a thickness-dependent spectral weight transfer from the high-energy collective modes to the low-energy single-particle excitations, until the bulk plasmon ceases to exist below 5 ML. These results are striking manifestations of the role of quantum confinement on plasmon resonances in precisely controlled nanostructures. They furthermore suggest the intriguing possibility of tuning resonant plasmon frequencies via precise dimensional control.