  We conduct a systematic study of the impact of new physics in quark-level $b
\to c \bar{c} s$ transitions on $B$-physics, in particular rare $B$-decays and
$B$-meson lifetime observables. We find viable scenarios where a sizable effect
in rare semileptonic $B$-decays can be generated, compatible with experimental
indications and with a possible dependence on the dilepton invariant mass,
while being consistent with constraints from radiative $B$-decay and the
measured $B_s$ width difference. We show how, if the effect is generated at the
weak scale or beyond, strong renormalisation-group effects can enhance the
impact on semileptonic decays while leaving radiative $B$-decay largely
unaffected. A good complementarity of the different $B$-physics observables
implies that precise measurements of lifetime observables at LHCb may be able
to confirm, refine, or rule out this scenario.
