  We present a family-non-universal extension of the Standard Model where the
the first two families feature both quark-lepton and electroweak-flavour
unification, via the $SU(4) \times Sp(4)_L \times Sp(4)_R$ gauge group, whereas
quark-lepton unification for the third family is realised \`a la Pati-Salam.
Via staggered symmetry breaking steps, this construction offers a natural
explanation for the observed hierarchical pattern of fermion masses and
mixings, while providing a natural suppression for flavour-changing processes
involving the first two generations. The last-but-one step in the
symmetry-breaking chain is a non-universal 4321 model, characterised by a
vector leptoquark naturally coupled mainly to the third generation. The
stability of the Higgs sector points to a 4321$\to$SM symmetry-breaking scale
around the TeV, with interesting phenomenological consequences in $B$ physics
and collider processes that differ from those of other known 4321 completions.
