  We show that the rate for di-Higgs production at the LHC can be enhanced by a
factor as large as 25 compared to the Standard Model value in the two Higgs
doublet model while being consistent with the known properties of the observed
Higgs boson $h$. There are correlated modifications in $t\overline{t}h$ and
resonant $Zh$ production rates, which can serve as tests of this model. Our
framework treats both Higgs doublets on equal footing, each with comparable
Yukawa couplings to fermions. The Cheng-Sher ansatz for multi-Higgs doublet
model is shown to be strongly disfavored by current experiments. We propose a
new ansatz for the Yukawa couplings of the Higgs doublets $\Phi_a$ is proposed,
where $Y_{ij}^{(a)} = C_{ij}^{(a)}\cdot {\rm min}\{m_i, \, m_j\}/v$, with
$C_{ij}^{(a)}$ being order one coefficients, $m_i$ the mass of fermion $i$ and
$v$ the electroweak vacuum expectation value. Such a pattern of couplings can
explain the observed features of fermion masses and mixings and satisfies all
flavor violation constraints arising from the exchange of neutral Higgs bosons.
The rate for $\mu \rightarrow e \gamma$ decay and new contributions to CP
violation in $B_s-\overline{B}_s$ mixing are predicted to be close to the
experimental limits.
