  We consider the effects of strong dissipation in quantum systems with a
notion of locality, which induces a hierarchy of many-body relaxation
timescales as shown in [Phys. Rev. Lett. 124, 100604 (2020)]. If the strength
of the dissipation varies strongly in the system, additional separations of
timescales can emerge, inducing a manifold of metastable states, to which
observables relax first, before relaxing to the steady state. Our simple model,
involving one or two "good" qubits with dissipation reduced by a factor
$\alpha<1$ compared to the other "bad" qubits, confirms this picture and admits
a perturbative treatment.
