  We present new circular Wilson loops in three-dimensional N=4 quiver
Chern-Simons-matter theory on S^3. At any given node of the quiver, a
two-parameter family of operators can be obtained by opportunely deforming the
1/4 BPS Gaiotto-Yin loop. Including then adjacent nodes, the coupling to the
bifundamental matter fields allows to enlarge this family and to construct loop
operators based on superconnections. We discuss their classification, which
depends on both discrete data and continuous parameters subject to an
identification. The resulting moduli spaces are conical manifolds, similar to
the conifold of the 1/6 BPS loops of the ABJ(M) theory.
