  The collection of a few anomalies in semileptonic $B$-decays, especially in
$b\rightarrow c \tau \bar{\nu}$, invites to speculate about the emergence of
some striking new phenomena, perhaps interpretable in terms of a weakly broken
$U(2)^n$ flavor symmetry and of leptoquark mediators. Here we aim at a partial
UV completion of this interpretation by generalizing the minimal composite
Higgs model to include a composite vector leptoquark as well.
