  We consider more than one pair of SU(2)_L doublet Higgs supermultiplets in a
generic supersymmetric extension of the standard model, and calculate their
one-loop contributions to the soft mass insertions delta_{LL} etc. We find that
if large supersymmetry breaking in this sector is realized, the loop effects
can give rise to large contributions to the soft mass insertions, meaning that
they
  We apply our result to a recently proposed model based on the discrete Q_6
family group, and calculate the non-diagonal matrix element M_{12} of the
neutral meson systems. We focus our attention on the extra phases
phi_{d,s}^Delta in B_{d,s}-mixing and flavor-specific CP-asymmetries
a_{sl}^{d,s} in neutral B decays and obtain values that can be about one order
of magnitude larger than the standard model predictions. Our final results are
comparable with the recent experimental observations at D0 and CDF, but they
are still about a factor of 5 smaller than the recently measured dimuon
asymmetry from D0.
