  We discuss how multichannel Kondo physics can arise in the setting of a
localized level coupled to several bosonic Tomonaga-Luttinger liquid leads. We
propose one physical realization involving ultracold bosonic atoms coupled to
an atomic quantum dot, and a second, based on superconducting nanowires coupled
to a Cooper-pair box. The corresponding zero-temperature phase diagram is
determined via an interplay between Kondo-type phenomena arising from the dot
and the consequences of direct inter-lead hopping, which can suppress the Kondo
effect. We demonstrate that the multichannel Kondo state is stable over a wide
range of parameters. We establish the existence of two nontrivial phase
transitions, involving a competition between Kondo screening at the dot and
strong correlations either within or between the leads (which respectively
promote local number- and phase-pinning). These transitions coalesce at a
self-dual multicritical point.
