  We show how one may classify all semisimple algebras containing the
$\mathfrak{su}(3)\oplus \mathfrak{su}(2) \oplus \mathfrak{u}(1)$ symmetry of
the Standard Model and acting on some given matter sector, enabling theories
beyond the Standard Model with unification (partial or total) of symmetries
(gauged or global) to be catalogued. With just a single generation of Standard
Model fermions plus a singlet neutrino, the only gauged symmetries correspond
to the well-known algebras $\mathfrak{su}(5)$, $\mathfrak{so}(10),$ and
$\mathfrak{su}(4)\oplus \mathfrak{su}(2) \oplus \mathfrak{su}(2)$, but with two
or more generations a limited number of exotic symmetries mixing flavor, color,
and electroweak symmetries become possible. We provide a complete catalogue in
the case of 3 generations or fewer and describe how the method can be
generalized to include additional matter.
