  We discuss ground state factorization schemes in spin $S$ arrays with general
$XYZ$ couplings under general magnetic fields, not necessarily uniform or
transverse. It is first shown that given arbitrary spin alignment directions at
each site, nonzero couplings between any pair and fields at each site always
exist such that the ensuing Hamiltonian has an exactly separable eigenstate
with the spins pointing along the specified directions. Furthermore, by
suitable tuning of the fields this eigenstate can always be cooled down to a
nondegenerate ground state. It is also shown that in open one-dimensional
systems with arbitrary $XYZ$ first neighbor couplings, at least one separable
eigenstate compatible with an arbitrarily chosen spin direction at one site is
always feasible if the fields at each site can be tuned. We demonstrate as well
that in the vicinity of factorization, i.e., for small perturbations in the
fields or couplings, pairwise entanglement reaches full range. Some noticeable
examples of factorized eigenstates for uniform couplings are unveiled. The
present results open the way for separable ground state engineering. A notation
to quantify the complexity of a given type of solution according to the
required control on the system couplings and fields is introduced.
