  While the properties of the observed Higgs boson agree with the Standard
Model predictions, the hierarchy of fermion masses lacks an explanation within
the model. In this work, we propose a fresh approach to this problem, involving
a different Higgs doublet responsible for each quark mass. We construct a model
with a gauged, non-anomalous $U(1)$ family symmetry that fixes which fermion
couples to which doublet with an $\mathcal{O}(1)$ Yukawa coupling. The
hierarchy of masses is generated by the hierarchy of vacuum expectation values
of the Higgs fields. The model generically predicts a light, weakly coupled
pseudoscalar. We verify that the model satisfies constraints from flavour
changing neutral currents, Higgs phenomenology and electroweak precision tests.
