  The scale of mass generation for fermions (including neutrinos) and the scale
for electroweak symmetry breaking (EWSB) can be bounded from above by the
unitarity of scattering involving longitudinal weak gauge bosons or their
corresponding would-be Goldstone bosons. Including the exact n-body phase space
we analyze the 2 --> n ($n \geq 2$) processes for the fermion-(anti)fermion
scattering into multiple gauge boson final states. Contrary to naive energy
power counting, we demonstrate that as $n$ becomes large, the competition
between an increasing energy factor and a phase-space suppression leads to a
{\it strong new upper bound} on the scale of fermion mass generation at a
finite value $n=n_s$, which is {\it independent of the EWSB scale,} $v =
(\sqrt{2}G_F)^{-1/2}$. For quarks, leptons and Majorana neutrinos, the
strongest 2 --> n limits range from about 3TeV to 130-170TeV (with $2\lesssim
n_s \lesssim 24$), depending on the measured fermion masses. Strikingly, given
the tiny neutrino masses as constrained by the neutrino oscillations,
neutrinoless double-beta decays and astrophysical observations, the unitarity
violation of $\nu_L\nu_L\to nW_L^a$ scattering actually occurs at a scale no
higher than ~170 TeV. Implications for various mechanisms of neutrino mass
generation are analyzed. On the other hand, for the 2 --> n pure
Goldstone-boson scattering, we find that the decreasing phase space factor
always dominates over the growing overall energy factor when $n$ becomes large,
so that the best unitarity bound on the scale of EWSB remains at n=2.
