  For stratified Mukai flops of type $A_{n,k}, D_{2k+1}$ and $E_{6,I}$, it is
shown the fiber product induces isomorphisms on Chow motives. In contrast to
(standard) Mukai flops, the cup product is generally not preserved. For $A_{n,
2}$, $D_5$ and $E_{6, I}$ flops, quantum corrections are found through
degeneration/deformation to ordinary flops.
