  We study theoretically the deformation of the Fermi surface (FS) of a three
dimensional gas of Rydberg-dressed $^6$Li atoms. The laser dressing to
high-lying Rydberg $D$-states results in angle-dependent soft-core shaped
interactions whose anisotropy is described by multiple spherical harmonics. We
show that this can drastically modify the shape of the FS and that its
deformation depends on the interplay between the Fermi momentum $k_F$ and the
reciprocal momentum $\bar{k}$ corresponding to the characteristic soft-core
radius of the dressing-induced potential. When $k_F< \bar{k}$, the dressed
interaction stretches a spherical FS into an ellipsoid. When $k_F\gtrsim
\bar{k}$, complex deformations are encountered which exhibit multipolar
characteristics. We analyze the formation of Cooper pairs around the deformed
FS, and show that they occupy large orbital angular momentum states ($p$-, $f$-
and $h$-wave) coherently. Our study demonstrates that Rydberg-dressing to high
angular momentum states may pave a route towards the investigation of
unconventional Fermi gases, and multiwave superconductivity.
