  For every parabolic subgroup $P$ of a Lie supergroup $G$ the homogeneous
superspace $G/P$ carries a $G$-invariant supergeometry. We address the quesiton
whether $\mathfrak{g}=\operatorname{Lie}(G)$ is the maximal symmetry of this
supergeometry in the case of exceptional Lie superalgebras $G(3)$ and $F(4)$.
Our approach is to consider the negatively graded Lie superalgebras for every
choice of parabolic, and to compute the Tanaka-Weisfeiler prolongations, with
reduction of the structure group when required (2 resp 3 cases), thus realizing
$G(3)$ and $F(4)$ as symmetries of supergeometries. This gives 19 inequivalent
$G(3)$-supergeometries and 55 inequivalent $F(4)$-supergeometries, in majority
of cases (17 resp 52 cases) those being encoded as vector superdistributions.
We describe those supergeometries and realize supersymmetry explicitly in some
cases.
