  A method is proposed to extend the zero-temperature Hall-Klemm microscopic
theory of the Knight shift $K$ in an anisotropic and correlated, multi-band
metal to calculate $K(T)$ at finite temperatures $T$ both above and into its
superconducting state. The transverse part of the magnetic induction ${\bf
B}(t)={\bf B}_0+{\bf B}_1(t)$ causes adiabatic changes suitable for treatment
with the Keldysh contour formalism and analytic continuation onto the real
axis. We propose that the Keldysh-modified version of the Gor'kov method can be
used to evaluate $K(T)$ at high ${\bf B}_0$ both in the normal state, and by
quantizing the conduction electrons or holes with Landau orbits arising from
${\bf B}_0$, also in the entire superconducting regime for an anisotropic,
multiband Type-II BCS superconductor. Although the details have not yet been
calculated in detail, it appears that this approach could lead to the simple
result $K_S(T)\approx a({\bf B}_0)-b({\bf B}_0)|\Delta({\bf B}_0,T)|^2$, where
$2|\Delta({\bf B}_0,T)|$ is the effective superconducting gap. More generally,
this approach can lead to analytic expressions for $K_S(T)$ for anisotropic,
multiband Type-II superconductors of various orbital symmetries that could aid
in the interpretation of experimental data on unconventional superconductors.
