The measurement of a large like-sign dimuon asymmetry A §L by the DO experiment at the Tevatron departs noticeably from Standard Model (SM) expectations and it may be interpreted as a hint of physics beyond the Standard Model contributing to AB ^ 0 transitions. In this work we analyze how the natural suppression of A$L in the SM can be circumvented by new physics. We consider generic Standard Model extensions where the charged current mixing matrix is enlarged with respect to the usual 3 x 3 unitary Cabibbo-Kobayashi-Maskawa matrix, and show how, within this framework, a significant enhancement over Standard Model expectations for A h SL is easily reachable through enhancements of the semileptonic asymmetries A(?L and AJL of both B°d-B°d and B°-B°s systems. Despite being insufficient to reproduce the DO measurement, such deviations from SM expectations may be probed by the LHCb experiment.