  We made heat-capacity measurements of two dimensional (2D) $^3$He adsorbed on
graphite preplated with monolayer $^4$He in a wide temperature range (0.1 $\leq
T \leq$ 80 mK) at densities higher than that for the 4/7 phase (= 6.8
nm$^{-2}$). In the density range of 6.8 $\leq \rho \leq$ 8.1 nm$^{-2}$, the 4/7
phase is stable against additional $^3$He atoms up to 20% and they are promoted
into the third layer. We found evidence that such promoted atoms form a
self-bound 2D Fermi liquid with an approximate density of 1 nm$^{-2}$ from the
measured density dependence of the $\gamma$-coefficient of heat capacity. We
also show evidence for the first-order transition between the commensurate 4/7
phase and the ferromagnetic incommensurate phase in the second layer in the
density range of 8.1 $\leq \rho \leq$ 9.5 nm$^{-2}$.
