Recent torsional oscillator measurements on the second layer of  ^{$4^{}$}${\mathrm{He }}^{}$${\mathrm{}}^{}$adsorbed on graphite have identified an anomalous superfluid response over a coverage range near third-layer promotion, with four distinct coverage regimes. Here, we present details of the superfluid response in the coverage regime immediately below third-layer promotion. A scaling analysis of the inferred superfluid fraction shows the characteristic temperature governing the superfluid response to decrease, approaching zero near the coverage at which simulations predict the second layer to form a conventional incommensurate solid.