  We propose and study a setup realizing a stable manifold of non-Fermi liquid
states. The device consists of a mesoscopic superconducting island hosting $N
\ge 3$ Majorana bound states tunnel-coupled to normal leads, with a Josephson
contact to a bulk superconductor. We find a nontrivial interplay between
multi-channel Kondo and resonant Andreev reflection processes, which results in
the fixed point manifold. The scaling dimension of the leading irrelevant
perturbation changes continuously within the manifold and determines the
power-law scaling of the temperature dependent conductance.
