  We present new trial wave-functions which include 3-body correlations into
the backflow coordinates and a 4-body symmetric potential. We show that our
wavefunctions lower the energy enough to stabilize the ground state energies of
normal liquid $^3$He in the unpolarized state at all pressures in agreement
with experiment; however, quantitative discrepancies remain. Further, we
include strong spin coupling into the Fermi liquid by adapting pairing wave
functions. We demonstrate a new, numerically stable method to evaluate pairing
functions which is also useful for Path Integrals calculations at low, but
non-zero temperatures.
