  The measurement by the D0 collaboration of a large like-sign dimuon asymmetry
deviates significantly from Standard Model expectations. New Physics may be
invoked to account for such a deviation. We analyse how generic extensions of
the Standard Model where the Cabibbo-Kobayashi-Maskawa $3\times 3$ mixing
matrix is enlarged can accommodate a significant enhancement of $A^b_{SL}$ with
respect to standard expectations through enhancements of the individual
semileptonic asymmetries $A^d_{SL}$ and $A^s_{SL}$ in the $B^0_d$-$\bar B^0_d$
and $B^0_s$-$\bar B^0_s$ systems. The potential enhancement reachable in this
class of scenario is, nevertheless, insufficient to reproduce the D0
measurement.
