  We show that the affine cones over a general Fano-Mukai fourfold of genus
$g=7$, $8$ and $9$ are flexible. Equivalently, there is an infinitely
transitive action of the special automorphism group on such affine cones. In
particular, any Mukai fourfold of genus $7,8$ and $9$ is $\Bbb
A^2$-cylindrical.
