  We show how to induce pairing of Cooper pairs (and, thus, $4e$
superconductivity) as a result of local embedding of a quantum impurity in a
Josephson network fabricable with conventional junctions. We find that a
boundary double Sine-Gordon model provides an accurate description of the dc
Josephson current patterns, as well as of the stable phases accessible to the
network. We point out that tunneling of pairs of Cooper pairs is robust against
quantum fluctuations, as a consequence of the time reversal invariance, arising
when the central region of the network is pierced by a dimensionless magnetic
flux $\phi = \pi$. We find that, for $\phi = \pi$, a stable attractive finite
coupling fixed point emerges and point out its relevance for engineering a two
level quantum system with enhanced coherence.
