We revisited the phase diagram of the second layer of ^{4}He on top of graphite using quantum Monte Carlo methods. Our aim was to explore the existence of the novel phases suggested recently in experimental works, and determine their properties and stability limits. We found evidence of a superfluid quantum phase with hexatic correlations, induced by the corrugation of the first Helium layer, and a quasi-two-dimensional supersolid corresponding to a 7/12 registered phase. The 4/7 commensurate solid was found to be unstable, while the triangular incommensurate crystals, stable at large densities, were normal.
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