  By using the diffusion Monte Carlo method, we obtained the full phase diagram
of $^3$He on top of graphite preplated with a solid layer of $^4$He. All the
$^4$He atoms of the substrate were explicitly considered and allowed to move
during the simulation. We found that the ground state is a liquid of density
0.007 $\pm$ 0.001 \AA$^{-2}$, in good agreement with available experimental
data. This is significantly different from the case of $^3$He on clean
graphite, in which both theory and experiment agree on the existence of a
gas-liquid transition at low densities. Upon an increase in $^3$He density, we
predict a first-order phase transition between a dense liquid and a registered
7/12 phase, the 4/7 phase being found metastable in our calculations. At larger
second-layer densities, a final transition is produced to an incommensurate
triangular phase.
