  We perform global fits within Standard Model Effective Field Theory (SMEFT)
combining top-quark pair production processes and decay with $b\rightarrow s$
flavor changing neutral current transitions and $Z \to b \bar b$ in three
stages: using existing data from the LHC and $B$-factories, using projections
for the HL-LHC and Belle II, and studying the additional new physics impact
from a future lepton collider. The latter is ideally suited to directly probe
$\ell^+\ell^-\rightarrow t\bar t$ transitions. We observe powerful synergies in
combining both top and beauty observables as flat directions are removed and
more operators can be probed. We find that a future lepton collider
significantly enhances this interplay and qualitatively improves global SMEFT
fits.
