  We identify the dominant computational cost within the recently introduced
stochastic and internally contracted FCIQMC-NEVPT2 method for large active
space sizes. This arises from the contribution to the four-body intermediates
arising from low-excitation level sampled determinant pairs. We develop an
effective way to mitigate this cost via an additional stochastic step within
the sampling of the required NEVPT2 intermediates. We find this systematically
improvable additional sampling can reduce simulation time by 80\% without
introducing appreciable error. This saving is expected to increase for larger
active spaces. We combine this enhanced sampling scheme with full stochastic
orbital optimization for the first time, and apply it to find FCIQMC-NEVPT2
energies for spin states of an iron porphyrin system within (24,24) active
spaces with relatively meagre computational resources. This active space size
can now be considered as routine for NEVPT2 calculations of strongly correlated
molecular systems within this improved stochastic methodology.
