We report on torsional oscillator studies of superfluidity in the second and higher layers of He4 films adsorbed on basal plane graphite. Our measurements reveal several novel features. We observe a reentrant superfluid phase in the second layer of adsorbed helium. Superfluidity disappears before the completion of the second layer and reappears early in the third layer. A well-defined plateau in the transition temperature occurs at the beginning of the fourth layer.