  Appropriately identifying and treating molecules and materials with
significant multi-reference (MR) character is crucial for achieving high data
fidelity in virtual high throughput screening (VHTS). Nevertheless, most VHTS
is carried out with approximate density functional theory (DFT) using a single
functional. Despite development of numerous MR diagnostics, the extent to which
a single value of such a diagnostic indicates MR effect on chemical property
prediction is not well established. We evaluate MR diagnostics of over 10,000
transition metal complexes (TMCs) and compare to those in organic molecules. We
reveal that only some MR diagnostics are transferable across these materials
spaces. By studying the influence of MR character on chemical properties (i.e.,
MR effect) that involves multiple potential energy surfaces (i.e., adiabatic
spin splitting, $\Delta E_\mathrm{H-L}$, and ionization potential, IP), we
observe that cancellation in MR effect outweighs accumulation. Differences in
MR character are more important than the total degree of MR character in
predicting MR effect in property prediction. Motivated by this observation, we
build transfer learning models to directly predict CCSD(T)-level adiabatic
$\Delta E_\mathrm{H-L}$ and IP from lower levels of theory. By combining these
models with uncertainty quantification and multi-level modeling, we introduce a
multi-pronged strategy that accelerates data acquisition by at least a factor
of three while achieving chemical accuracy (i.e., 1 kcal/mol) for robust VHTS.
