  We analyse supersymmetric models augmented by an extra $U(1)$ gauge group. To
avoid anomalies in these models without introducing exotics, we allow for
family-dependent $U(1)^\prime$ charges, and choose a simple form for these,
dependent on one $U(1)^\prime$ charge parameter only. With this choice,
$Z^\prime$ decays into di-taus but not di-leptons, weakening considerably the
constraints on its mass. In the supersymmetric sector, the effect is to lower
the singlino mass, allowing it to be the dark matter candidate. We investigate
the dark matter constraints and collider implications of such models, with
mostly singlino, or mostly higgsinos, or a mixture of the two as lightest
supersymmetric particles. In these scenarios, $Z^\prime$ decays significantly
into chargino or neutralino pairs, and thus indirectly into final state
leptons. We devise benchmarks which, with adequate cuts, can yield signals
visible at the high-luminosity LHC.
