  We consider a 4-Higgs-doublet model in which each Higgs doublet gives mass to
one of the fermion sets $\{ m_t\}$, $\{ m_b,m_\tau,m_c \}$, $\{ m_\mu,m_s \}$,
and $\{ m_d,m_u,m_e \}$. The sets have the feature that within each of them the
masses are similar. Our model explains the mass hierarchies of the sets by
hierarchies of the vacuum expectation values of the Higgs doublets associated
to them. All Yukawa couplings are therefore of order one. Neutrino masses are
generated by a type-I seesaw mechanism with PeV-scale singlet neutrinos. To
avoid the appearance of tree-level flavor changing neutral currents, we assume
that all Yukawa matrices are singularly aligned in flavor space. We mean by
this that the Yukawa matrices are given as linear combinations of the rank $1$
matrices that appear in the singular value decomposition of the mass matrix. In
general, singular alignment allows to avoid flavor changing neutral currents in
models with multiple Higgs doublets.
