  We develop a generalized pseudo-fermion functional renormalization group
(PFFRG) approach that can be applied to arbitrary Heisenberg models with spins
ranging from the quantum case $S=1/2$ to the classical limit
$S\rightarrow\infty$. Within this framework, spins of magnitude $S$ are
realized by implementing $M=2S$ copies of spin-1/2 degrees of freedom on each
lattice site. We confirm that even without explicitly projecting onto the
highest spin sector of the Hilbert space, ground states tend to select the
largest possible local spin magnitude. This justifies the average treatment of
the pseudo fermion constraint in previous spin-1/2 PFFRG studies. We apply this
method to the antiferromagnetic $J_1$-$J_2$ honeycomb Heisenberg model with
nearest neighbor $J_1>0$ and second neighbor $J_2>0$ interactions. Mapping out
the phase diagram in the $J_2/J_1$-$S$ plane we find that upon increasing $S$
quantum fluctuations are rapidly decreasing. In particular, already at $S=1$ we
find no indication for a magnetically disordered phase. In the limit
$S\rightarrow\infty$, the known phase diagram of the classical system is
exactly reproduced. More generally, we prove that for $S\rightarrow\infty$ the
PFFRG approach is identical to the Luttinger-Tisza method.
