  The recently reported measurements of the CP asymmetry a(psi K) by the BABAR
and BELLE collaborations are in good agreement with the standard model (SM)
prediction, resulting from the unitarity of the CKM matrix. The so-called
minimal flavour violating (MFV) supersymmetric extensions of the standard
model, in which the CKM matrix remains the only flavour changing structure,
predict a(psi K) similar to the one in the SM. With the anticipated precision
in a(psi K) and other CP asymmetries at the B factories and hadron colliders,
one hopes to pin down any possible deviation from the SM. We discuss an
extension of the MFV-supersymmetric models which comfortably accommodates the
current measurements of the CP asymmetry a(psi K), but differs from the SM and
the MFV-supersymmetric models due to an additional flavour changing structure
beyond the CKM matrix. We suggest specific tests in forthcoming experiments in
B physics. In addition to the CP-asymmetries in B-meson decays, such as a(psi
K) and a(pi pi), and the mass difference Delta M_s in the Bs-bar(Bs) system, we
emphasize measurements of the radiative transition b -> d gamma as sensitive
probes of the postulated flavour changing structure. Interestingly, the
CKM-unitarity analysis in the Extended-MFV model also allows solutions rho < 0,
as opposed to the SM and the MFV models for which only rho > 0 solutions are
now admissible, implying gamma > pi/2, where gamma=- arg (Vub). Such large
values of gamma are hinted by the current measurements of the branching ratios
for the decays B -> pi pi and B -> K pi.
