  The Standard Model (SM) is a chiral theory, where right- and left-handed
fermion fields transform differently under the gauge group. Extra fermions, if
they do exist, need to be heavy otherwise they would have already been
observed. With no complex mechanisms at work, such as confining interactions or
extra-dimensions, this can only be achieved if every extra right-handed fermion
comes paired with a left-handed one transforming in the same way under the
Standard Model gauge group, otherwise the new states would only get a mass
after electroweak symmetry breaking, which would necessarily be small
($\sim100\textrm{ GeV}$). Such a simple requirement severely constrains the
fermion content of Grand Unified Theories (GUTs). It is known for example that
three copies of the representations $\mathbf{\overline{5}}+\mathbf{10}$ of
$SU(5)$ or three copies of the $\mathbf{16}$ of $SO(10)$ can reproduce the
Standard Model's chirality, but how unique are these arrangements? In a
systematic way, this paper looks at the possibility of having non-standard
mixtures of fermion GUT representations yielding the correct Standard Model
chirality. Family unification is possible with large special unitary groups ---
for example, the $\mathbf{171}$ representation of $SU(19)$ may decompose as
$3\left(\mathbf{16}\right)+\mathbf{120}+3\left(\mathbf{1}\right)$ under
$SO(10)$.
