  We consider a deformation of the Third Family Hypercharge Model, which
arguably makes the model more natural. Additional non-zero charges of the
spontaneously broken, family-dependent $U(1)_F$ gauge symmetry are assigned to
the second family leptons, and the third family leptons' charges are deformed
away from their hypercharges in such a way that the $U(1)_F$ gauge symmetry
remains anomaly-free. Second family $U(1)_F$ lepton charges allow a $Z^\prime$
coupling to muons without having to assume large charged lepton mixing, which
risks violating tight lepton flavour violation bounds. In this deformed
version, only the bottom and top Yukawa couplings are generated at the
renormalisable level, whereas the tauon Yukawa coupling is absent. The
$Z^\prime$ mediates a beyond the Standard Model contribution to an effective
$(\bar b s) (\bar \mu \mu)$ vertex in the combination $C_9=-9C_{10}$ and is
able to fit the apparent discrepancy between Standard Model predictions in
flavour changing neutral-current $B-$meson decays and their measurements,
whilst simultaneously avoiding current constraints from direct $Z^\prime$
searches and other measurements, when $1.2\ \text{TeV} < M_{Z^\prime} < 12.5\
\text{TeV}$.
